Top page ( Quantum mechanics and Einstein relativity are wrong )

Successful QED anomalous magnetic momnet is just a wrong math trick.

Particle physics, standard model is full of fictional concepts

Relativistic Dirac hydrogen fine structure is wrong.

- Fictitious photon-electron interaction term uses wrong math
- Relativistic Klein-Gordon equation (= Higgs ? ) failed
- Relativistic Dirac equation describes electrons unrealistically
- Photon doesn't exist. It's only a "mathematical" product.

*(Fig.1) Relativistic quantum field theory is a nonphysical abstract "Math" with No real particle description.*

Quantum field theory and QED are just a nonphysical useless abstract math theory irrelevant to our real world.

The present useless quantum field theory was artificially created by combining the fantasy quantum mechanics and paradoxical Einstein relativity to lead to **nonphysical** quantum electrodynamics (= QED ), standard model and extra-dimensional string theory (= unreal "theory of everything" ).

All the present quantum field theory (= QFT ) and QED are completely useless, they only describe particles such as electrons and (fictitious) photons as **nonphysical** abstract math symbols (= each electron or photon is expressed just as meaningless math symbols = a^{†}, b^{†}, c^{†}.. ) with **No** concrete figures ( this p.69-72, this p.23-52 ), contrary to the media's falsely colorful pictures of (imaginary) particles

**Un**physical quantum field theory and QED describe all interaction (= forces ) between (fictitious) particles as nonphysical abstract Feynman diagram ( this p.39-44 ) whose interaction must be always mediated by **unreal** virtual particles with imaginary mass ( this p.9 ) contradicting Einstein relativistic mass ( this p.3 this p.5 ). ← The present particle physics is self-**contradictory**, so false.

**All** calculated values by these nonphysical quantum field theory and QED miserably **diverge** to "meaningless infinity" due to unreal infinite virtual particles allegedly having infinite energies and momentums ( this p.64 (or p.68 ) ).

So physicists had to rely on illegitimate methods called "renormalization" where the calculated meaningless infinity allegedly caused by infinite quantum virtual particles and virtual photons should be artificially **canceled out by another artificially-created infinity** (= invisible infinite bare charge and mass of an electron, this p.4-5 ) to obtain the convenient finite values such as the anomalous magnetic moment (= g-factor ) and Lamb shift ( this 4th~ paragraphs, this p.4-6, this p.1-right, this p.4-right ).

↑ Of course, this ad-hoc illegitimate renormalization **artificially removing infinity** is a wrong useless math just manipulating free parameters with No ability to predict any physical values ( this p.3-left ), which were harshly criticized even by founders such as Dirac and Feynman as "hocus-pocus, dippy process ( this p.2 )."

Actually, **Nobody** uses this useless quantum field theory, QED and (unreal) virtual particles in actual applied technology.

The present quantum field theory is very complicated (= but its fundamental principle is simply **broken** as "infinity" allegedly caused by unreal virtual particles ) and takes much time to learn.

( I aimed to make this page simple and easy to understand. )

If you believe this quantum field thoery is true and can give fundamental answers about our nature, you will be surely **disappointed** that this theory has **NO** clear and physical images, and is only "**mathematical**" language after learning it for a long time.

On this page, we explain this fact as clearly as possible.

*(Fig.2) Einstein relativistic energy-momentum relation + quantum mechanics = quantum field theory (= Klein-Gordon equation ).*

According to the special relativity, when the object is moving at the velocity of " **u** ", its mass supposedly appears to be heavier.

This Einstein strange relation of mass (= m ), energy (= E ) and momentum (= p ) leads to the Einstein famous relativistic mass, energy-momentum relation, which is the basis of all the relativistic quantum field theory and QED.

The problem is this Einstein relativistic energy-momentum relation contains serious paradoxes where the particle's objects "look" heavier or lighter as seen by different observers moving at different speeds ( this p.48-49 ), though the observers don't touch the objects. ← Impossible

Furthermore, all the quantum field theory and QED have to rely on (unreal) virtual particles as virtual mediator of forces and interactions between particles using abstract Feynman diagram.

These (unreal) virtual particles indispensable for relativistic quantum field theory disobey the Einstein relativistic mass or energy-momentum relation, so the current relativistic quantum field theory is self-**contradictory**, and worng.

In fact, This relativistic mass relation of mc^{2} was **Not** the original idea of Einstein who just copied the **already-existing** Maxwell's authentic classical energy = mc^{2} in the wrong way.

According to unrealistic Einstein relativity, energy (= E ) and momentum (= p ) can be freely changed as seen by different observers moving at different speeds (= supernatural Lorentz transformation of special relativity )

These relativistically-changeable (pseudo-)energy E and three momentums (= px, py, pz ) are called four-momentum or four-vectors (= ct, x, y, z )

*(Eq.0-1)*

These four momentums satisfy energy-momentum relation of Fig.2, from which all quantum field theories **start**.

And the equation of Fig.2 holds in **any veclocity** "u", so Fig.2 is called "Lorentz-invariant **scalar**".

"Scalar" means they do not change under Lorentz transformation, In this case, the rest mass energy (= m_{0}c^{2} ) is Lorentz invariant scalar which is unchanged as seen by different observers ( this p.6-upper, this p.3 ).

This relativistic property is **broken** when physicists move from free particles with No external potential energies to actual atomic energies under external Coulomb potential energies (= Coulomb law is **Not** relativistic or Lorentz invariant form ), so Einstein relativity and relativistic quantum field theory can **Not** apply to the real world phenomena, hence, wrong.

*(Eq.0-2) Relativistic energy-momentum → quantum Klein-Gordon equation.*

The 1st proposed relativistic quantum field theory is Klein-Gordon equation which was obtained by replacing the momentum p with de Broglie wave derivative operator in Einstein's original relativistic energy-momentum relation ( this p.2 ).

Klein-Gordon equation (= called scalar field ) is said to express the spin-0 particles such as (fictitious) Higgs boson, and their virtual particles.

The problem is that Einstein relativistic energy momentum relation (= or Klein-Gordon equation ) has the second-order energy (= E^{2} = p^{2} + .. ), which is useless and unable to be added to Coulomb potential energy for getting the ordinary first-order total energy term (= total energy E = kinetic + Coulomb potential energy, this 13th-paragraph ).

Relativistic quantum field theory such as Klein-Gordon equation just describes each particle as nonphysical math symbols with No concrete physical shapes, and its virtual particles give unrealistic infinite energies ( this p.21-25 ).

Quantum field theory can do **nothing** except for very simple meaningless task of just creating or annihilating each particle (= a^{†}(p) or field ) with infinitely-uncertain momentum p ( and energy ) in all uncertain positions of the vaccum ( this p.23-26 ), which abstract math theory has No ability to describe actual physical phenomena where various particles with some finite momentums are moving around in various different (definite) positions.

Quantum mechanics united with Einstein special relativity (= energy-momentum relation ) to form the nonphysical relativistic quantum field theory such as Klein-Gordon and Dirac equation.

The problem is all these relativistic quantum field theories always have to contain infinite numbers of (virtual) particles with infinite momentums and energies ( this p.4-5 ) to satisfy the unreasonable Einstein relativistic demand ( this 2nd-paragraph, this 11-12th paragraphs, this 4th~ paragraphs ), which unreasonably strict relativistic condition is called Lorentz invariance (= particles' motions must look the same = infinite momentum or velocity looks the same infinite, as seen by any observers moving at any velocities, like virtual particle's infinite momentum ∞ + finite momentum by observers remains the same infinite momentum ∞ = unrealistic Lorentz invariance ).

Though the present relativistic quantum field theory represented by Dirac equation has already **violated** this relativistic condition in the (fictitious) spin-orbit interaction (= basis of quantum mechanical fine structure ) where the orbital angular momentums are magically changed as seen by differently-moving observers = paradox ! ← The present relativistic quantum field theory is self-contradictory and **wrong**.

These unrealistic "relativistic" infinite virtual particles with infinite momentums and energies always give the meaningless infinite values called "ultraviolet divergence" in **all** calculations of relativistic QFT, QED and particle physics ( this 15th-paragraph~, this p.34, this p.6, this p.14, this p.10 ).

So all calculation processes in relativistic quantum field theory or QED is

Einstein relativity + quantum mechanics = unreal infinite virtual particles with infinite energies ( this p.2-middle ) which virtual pseudo-particles are allegedly mediators of all interactions → All calculation values always diverge to meaningless **infinity** → Infinity must be artificially canceled by another "freely-adjustable infinity (= bare charge, this 26th-paragraph )" using illegitimate math tricks called "renormalization", which ad-hoc QED was criticized even by founders such as Dirac and Feynman ( this 1st-paragraph, this last-paragraph )

*(Eq.0-3) Dirac equation = 1st-order energy (= E or p ^{0} ) and momentum (= p^{j} ) equation using nonphysical complex numbers i and matrix γ.*

The original Einstein relativistic energy (= E ) momentum (= p ) equation and Klein-Gordon equation consist of the inconvenient 2nd-order energy and momentum terms (= E^{2} = p^{2} + m^{2} ), which equations are completely **useless**, because they cannot add the potential energy to the kinetic energy for obtaining 1st-order total energy (= E = kinetic + potential energies ).

So Dirac tried to obtain the "square root of this Einstein energy-momentum relation" with 1st-order energy and momentum (= E = p + m ). ← This Dirac's reckless attempt to get the square root of the relativistic energy-momentum relation is mathematically **impossible**.

Dirac had to rely on some "**cheating**" where nonphysical imaginary number (= i ) and matrix were artificially introduced to obtain the (**pseudo**-)square root of Einstein energy-momentum relation ( this p.4, this p.13, this p.5-8 ).

*(Eq.0-4) Dirac trick of "square root" of relativistic energy-momentum equation *

where p^{j} ( j=1,2,3 or j=x,y,z components ) is the particle's momentum expressed as the de Broglie wave-type derivative -id/dx^{i} (= i is imaginary number ) and

*(Eq.0-5) *

where σ is 2 × 2 Pauli matrices.

↑ These artificially-introduced 4 × 4 γ matrices have **nothing** to do with the original quantum "spin" allegedly expressed by nonphysical 2 × 2 Pauli matrices.

But physicists started to **baselessly** insist these ( nonphysical and unrelated ) 4 × 4 γ matrices (= accidentaly obtained by doing the impossible square root of Einstein relativistic relation ) may indicate the quantum mechanical "spin" with No more detailed figure of "spin." ← Nonsense. Science **stops** progressing.

By (mis-)interpreting these meaningless math 4×4 γ matrices as irrelevant quantum mechanical "spin", physicists make the **baseless** bold claim that Dirac equation could describe all fermions such as electrons, quarks, neutrinos ( this p.4 ), antiparticles (= positrons ), and virtual particles. ← All calculations by this relativistic Dirac equation and unreal virtual particles miserably diverge to infinity.

All these fermions such as electrons, antiparticles, quarks are expressed as nonphysical abstract math symbols with No concrete figure in nonphysical relativistic quantum field theory represented by Dirac equation.

*(Eq.0-6) Nonphysical mechanism of Pauli exclusion principle = anticommutation where exchange of two particles (= c ) gives the minus sign ? ← No more detailed mechanism is given by the useless quantum mechanics !*

It is said that relativisic quantum field theory called Dirac equation can give the true mechanism of Pauli exclusion principle. ← **untrue**

All the nonphysical relativistic Dirac equation can do is present the very simple **abstract** math relation called "anticommutation" as the alleged Pauli principle mechanism, giving No more detailed mechanism ( this p.4-lower, this p.5-lower, this p.28 this p.4-6, ). ← Science stops progressing by stopping delving into deeper mechanism of Pauli repulsion.

Nonphysical quantum field theory represented by relativistic Dirac equation **failed** to explain the realistic mechanism of mysterious Pauli exclucion principle in detail.

Relativistic quantum mechanical Dirac equation just shows the meaningless abstract math relation called "anticommutation" as the alleged Pauli principle mechanism ( this p.7, this p.6 ). ← No more detailed mechanism is shown, so useless theory.

In this unphysical "anticommutation" Pauli principle, when two fermions (= electron, quark, antiparticle.. ) expressed as nonphysical math symbols (= each fermion is expressed as a symbol "c(k)" ) are exchanged, the entire sign becomes minus. ← That's **all**, **No** more detailed mechanism of Pauli principle is shown in the useless relativistic quantum field theory !

When two fermions (= or two electrons = c1 and c2 ) or their variables are interchanged, the sign is flipped (= amticommutation Pauli principle ) like

c1c2 = -c2c1

When these two fermions (= or two electrons ) are the same (= c1 = c2 ), the entire equation gets **cancelled** out to be zero due to this nonphysical anticommutation Pauli principle rule, like

c1c2 = -c2c1 → when c1 = c2 → c1c1 = - c1c1 → 2c1c1 = 0 → c1 = 0 = Pauli principle !?

↑ No more detailed explanation of mysterious Pauli principle mechanism than this meaningless abstract math is shown in the useless quantum field theory, so our science **stops** delving into the deeper detailed truth.

As shown on this page, we have proved the quantum mechanical Pauli principle based on nonphysical anticommutation or antisymmetric exchange relation (= exchanging two electrons flips the entire sign = Pauli principle ? ) contains fatal **paradoxes**, so wrong.

*(Eq.0-7) Dirac Lagrangian (= L ) + (virtual) photon → QED divergence.*

Unrealistic quantum electrodynamics (= QED ) is generated by connecting relativistic Dirac equation including electrons (and antiparticles ) and quantized Maxwell equation (= vector potential A ) including nonphysical (virtual) photons particles.

QED gives only the very simple (useless) photon-electron interaction term putting Dirac's electrons (= ψ ) and virtual photon (= A ) side by side ( this p.6, this p.36,40, this p.3 ). ← Useless QED can give no more detailed physical mechanism of how electrons interact with (virtual) photons, which uncertain interaction can be expressed as abstract Feynman diagram ( this p.3-4, this p.7-9, this p.24-25 ).

It is known that electrons can interact only with **unreal** virtual photons with imaginary mass ( this p.3 ), when the total energy and momentum are conserved (= energy-momentum conservation law is necessary also in relativistic QED, this p.5-6, this p.16, this 3rd-paragraph ), which unreal virtual photons disagree with Einstein relativistic mass ( this p.3, this p.5 ) ← self-contradiction !

Under Einstein's unreasonable relativistic condition, each particle must have infinite kinds of momentums and energies, hence, these infinite (virtual) energies always give meaningless infinite values in QED ( this p.13, this p.70, this p.64-lower, this p.31-32 ).

↑ So all the particle physics such as the relativistic quantum field theory, QED and standard model can only generate the **meaningless infinity** as calculation results, and physicists try to add another freely-adjustable infinity (= infinite bare charge, this p.4-5, this p.22-23 ) to cancel the infinite virtual particles' energies for obtaining some finite physical parameters (= anomalous magnetic moment ), which ad-hoc method called renormalization ( this p.7-11 ) is completely illegitimate and wrong in math and physics.

*(Eq.0-8) Weak force interaction via unreal virtual W boson is just a meaningless abstract math, Not physics. *

Not only electromagnetic forces but also all other fundamental forces such as (fictitious) weak, strong forces have to rely on unreal virtual particles in nonphysical quantum field theory.

Invisible W bosons (= alleged weak force mediator ) and invisible gluons (= strong force mediator ) are all unreal virtual particles ( this p.29 ).

Standard model or electroweak theory can only give abstract meaningless math or unphysical simple Feynman diagram as these imaginary particles' interactions ( this p.13, this p.78 ) like the electromagnetic force (= electron-virtual-photon interaction ).

And also in this (fictitious) weak force mediated by unreal virtual W boson, the calculation results **diverge** to meaningless infinity which must be artificially canceled out by another infinity using ad-hoc renormalization parameters ( this p.8 ).

In the nuclear strong force (= quantum chromodynamics or QCD theory ) between imaginary fractional-charge quarks and gluons, all calculations values diverge to infinity, which is too big to eliminate using the normal renormalization method (= perturbation method failed ) in Feynman diagram ( this p.18,26 ).

So physicists **threw away** the conventional quantum field theory and Feynman diagram, and invented the completely irrelevant nonphysical methods called lattice QCD with imaginary time and discontinuous space for calculating (imaginary) nuclear or quark property. ← The completely new ad-hoc lattice QCD **irrelevant** to the original quantum mechanics or QED perturbaion methods means quantum mechanics and quantum field theory **failed** to express nuclear force.

↑ All these nonphysical quantum field theory, QED, standard model and lattice QCD are completely **useless** in any applied science due to their **lack of reality** as seen in their unreal virtual particle-mediated interactions.

Standard model is self-contradictory.

**Massive** W boson meadiating weak force ( this p.17 ) has to be **massless** to renormalize or cancel their infinity (= caused by infinite unreal virtual particles ).

↑ To solve this contradiction, (imaginary) Higgs particle was invented to fictitiously lend "mass" to massless W boson, though this standard model's (unseen) Higgs tells us **nothing** about the detailed mechanism of how (imaginary) Higgs gives mass to other particles, except just showing **nonphysical** abstract math ( this p.23-34 )

*(Fig.4) An initial electron at rest (= p ) absorbs unreal virtual photon (= q ).*

Here we explain why a photon model (= a fictitious quantum particle of classical light wave ) proposed by Einstein **failed**.

Total energy (= E ) and momentum (= p ) must be always **conserved** also in (unphysical) relativistic quantum field theory or QED ( this p.6, this p.4-lower, this p.6 ).

But when an electron at rest (= having only rest mass energy = mc^{2}, with no momentum ( px, py, pz ) = ( 0, 0, 0 ) ) absorbs a photon ( with momentum q ) conserving the total energy and momentum (= p' = p + q ), this photon must always become an **unreal** virtual photon with imaginary mass (= square of a virtual photon's mass is negative, m^{2} < 0, this 14.7.3 ).

So these (unreal) virtual photons indispensable for all relativistic quantum field theory or QED contradict Einstein's relativistic energy-momentum relation, meaning Einstein relativity is self-contradictory and **false**.

In other cases, this virtual photon mass is greater than zero, which also **contradicts** Einstein relativity with massless photon ( this 4th-paragraph ).

*(Eq.0-9) Einstein relativistic energy (= E ) momentum (= p ) relation*

An initial electron at rest (= energy E is rest mass energy = mc^{2}, and zero momentum p = 0 ) absorbs a (virtual) photon (= momentum q ) to become the final moving electron with the total energy E' and momentum p' ( p' > 0 )

energy conservation: E' = mc^{2} + a photon's energy (= q^{0}c )

momentum conservation: p' = 0 (= p ) + a photon momentum (= q^{i}, i = x,y,z )

From Fig.4 and the **conservation** of energy and momentum, the photon's energy and momentum (= q ) is the difference between the final (= p' ) and initial (= p ) electrons' energies and momentums,

*(Eq.0-10)*

A relativistic photon's mass must be zero, but from Eq.0-10 and Eq.0-9, and Einstein relativistic energy-momentum equation,

*(Eq.0-11) a (virtual ) photon's mass calculated from its energy and momentum*

Eq.0-11 means this photon's mass is imaginary number ( final energy E' of a moving electron is larger than the rest mass energy, E' > mc^{2} ) !

Because energy-momentum equation of Eq.0-11 must be zero or **less than** zero for real particles, according to Einstein relativistic equation.

*(Eq.0-12)*

So Eq.0-11 shows this virtual photon is an unreal **tachyon** with imaginary mass, which disobeys special relativity.

In spite of this fact, they often use this tachyon-like particles in the accelerator and QED.

As a result, relativistic quantum field theory includes **self-contradiction**.

In thre relativistic quantum field theory and QED, all physical phenomena and equations must be the same, seen by any differently-moving observers due to the lack of absolute space.

So the upper unreal virtual particles with imaginary mass must apply to all cases of the initial eletrons with all kinds of initial velocities. ← Relativistic quantum field theory and QED are **false**.

Though they unscientifically insist on the unreasonable **uncertainty principle** and try to allow the temporary violation of total energy conservation law, which contradicts the fact that all observed particles always conserve total energy and momentum (= unreal virtual particles must transmit and conserve these energy and momentum between distant particles in quantum field theory )

As a result, relativistic quantum field theory, QED, and standard model which need unreal virtual particles as transmitter of energy and momentum, is self-contradictory and **false**.

*(Fig.5) Lorentz-invariant scalar in Einstein special relativity.*

Einstein tried to unscientifically explain the constant light speed c seen by any observers moving at any speeds using the paradoxical special relativity, Lorentz transformation and unreal virtual particles instead of using real space medium.

In the "magical" Einstein relativistic world, the time (= t ) and space (= x,y,z ) magically get longer or shorter as seen by different observers moving at different speeds. Here, K' (= t',x',y',z' ) and K (= t,x,y,z ) observers' different spacetimes (= or K' and K reference frames ) are used.

In Fig.5 where an observer K' (= who sees the spacetime coordinate t',x',y',z' ) is moving at a speed of v in x direction relative to the stationary observer K (= who sees the coordinate t,x,y,z ), the light is emitted from the origin (= x=x'=0 at the time of t=t'=0 ) and after a while, detected at some time of t or t' in each frame ( K and moving K' frames ).

According to special relativity, its speed must be always "**c**" in any reference frames (= or seen by any observers moving at different speeds ).

So the equation of the last line in Fig.5 does NOT change in any reference frames using Lorentz transformation between two observers' spacetimes K=(t,x,y,z) and K'=(t',x',y',z'). this p.4-6, this p.3-6

This unchanged equation is called "**Lorentz-invariant scalar**" which is unchanged as seen by any observers or different frames (= K and K' ), like the unchanged object's rest mass energy (= m_{0}c^{2} ).

In the relativistic quantum field theories, we start from the **invariance of the action** S ( or Lagrangian = No physical meaning, this p.1-last ) to get the equation of motion.

So Lorentz-invariant action (or Lagrangian, which are artificially-created nonphysical concepts allegedly giving the relativistic quantum field equations ) based on invariant Einstein relativistic mass-energy-momentum relation is most important concept in the relativity.

*(Eq.1-1) Four-vector. t = time, (x,y,z) = space coordinate, c = light speed*

To express the relativistic relation and scalar like Fig.5, it is convenient to define the notation and rule of four-vector (= time variable =t, space variables = x, y, z ) as shown in Eq.1-1.

In Eq.1-1, when the index μ is at the **lower** position (= x_{μ} ), only the **zero** component ct (= light speed c × time variable t ) becomes **negative** ( x_{0} = - ct ).

Other space components ( μ = 1, 2, 3 = x, y, z ) do not change their sign depending on their index position.

*(Eq.1-1') *

This notation rule is called ( **-1, 1, 1, 1** ) version metric tensor ( this p.4 ).

( You can freely choose the different version of (+1, -1, -1, -1), as shown in appendix, this p.14-15 )

Using Eq.1-1, the equation of Fig.5 can be expressed as

*(Eq.1-2) *

The notation of Eq.1-2 is often used in the relativistic theory.

The Lorentz invariant scalar (= x_{μ}x^{μ} ) can be expressed as a combination of variables of lower and upper indices ( this p.2-3, this p.4 ).

When the same variable (= for example, μ ) is used twice in one term, it means the sum of four terms with respect to μ = 0, 1, 2, 3.

( Even when Σ symbol is omitted, its meaning remains the same. )

Here we define **Minkowski metric tensor**, as follows,

*(Eq.1-3)*

Using this metric tensor in four vector of Eq.1-1, we can change the index position ( x^{μ} → x_{μ} ), as follows,

*(Eq.1-4)*

In Eq.1-4, "ν" is used twice in one term, so it means the sum of four-terms with respect to ν = 0, 1, 2, 3.

Using the relation of Eq.1-4, the scalar equation of Eq.1-2 can be expressed as

*(Eq.1-5) *

According to the special relativity, the relativistic momentum and energy are supposed to behave as four momentum (= four-momentums transform like four-vectors, ct, x, y, z ) under Lorentz transformation.

*(Eq.1-6)*

Using Eq.1-6, the Lorentz-invariant energy-momentum relation of Fig.2 can be expressed as

*(Eq.1-7) *

Next we explain the derivative, which are differential operators allegedly meaning the energy (= time derivative ) and momentum (= space derivative ).

The partial **derivative** symbols of space coordinates (i = 1, 2, 3) are expressed as,

*(Eq.1-8)*

The sign of the space derivative (= i = 1,2,3 or x,y,z ) doesn't change depending on the index position.

The partial derivative of the zero component (= time ) is

*(Eq.1-9)*

where x^{0} = "ct".

Unlike Eq.1-1, when the index " 0 " is at the **upper** position, the time derivative becomes **negative**.

You should change these signs if you want to use the different metric of ( 1, -1, -1, -1 ) like this p.2, this p.10

where ρ_{e} is "charge density", and J means **current density**.

Eq.1-10 means ρ_{e} and J transfrom like the spacetime ( t, x, y, z ) under Lorentz transformation ( this p.11, this p.3 ),

*(Eq.1-10')*

The definition of Eq.1-10 is indispensable for the relativistic Lorentz force law and the relation between current and charge density.

But Eq.1-10 causes observer's **supernatural power** and fatal paradoxes, as shown in this.

Four currents of Eq.1-10 change harmonizing with four vector potentials ( A ).

Of course, these definitions were "**artificially**" introduced to combine special relativity and Maxwell equations.

*(Fig.6) True Lagrangian must contain potential energy (= V ), but relativistic free particle's fake Lagrangian such as Klein-Gordon and Dirac replaced potential energy by irrelevant rest mass energy. ← trick*

Relativistic quantum field theory (QFT) tried to "copy" the ordinary classical mechanical Lagrangian (= L ), which is equal to kinetic energy (= T ) minus potential energy (= V ), in order to obtain the irrelevant relativistic Hamiltonian (= total energy ) of free particles (= No potential energies ) in Klein-Gordon and Dirac equations.

The problem is there was **No** such thing as "relativistic Lagrangian" in 1920s.

Originally, the artificial energy-related concept = Lagrangian (or action ) itself had No physical meaning ( this p.1-last ), whose "ambiguous **unreality**" attracted more **unrealistic** relativistic quantum field theories.

Physicists tried to invent artificial (**fake**) Lagrangian for nonphysical relativistic quantum field theory such as Klein-Gordon and Dirac equations.

The original classical Lagrangian (= L ) should be equal to kinetic energy (= T ) minus (external Coulomb) potential energy (= V ) like L = T - V ( this p.1-2, this middle ).

But relativistic energy momentum relation and its quantum field version such as Klein-Gordon and Dirac equation deal only with free particles **without** the indispensable potential energy ( this p.8 ).

So the relativistic quantum field theory made up **fake** Lagrangian replacing the original (external) potential energy (= V ) by the **irrelevant** rest mass energy (= mc^{2} ) which is Not a potential energy (= accelerate the particle's motion ) or the true Lagrangian at all ( this p.3, this p.1 ).

↑ It means all the relativistic quantum field theories such as QED, Dirac and Klein-Gordon equations using **fake** Lagrangians are based on the **unfounded** assumption, hence illegitimate and wrong.

But the **unphysical** relativistic quantum field theory, which originally had **No** realistic meaning, wanted some artificially-created Lagrangians (= L ) as a "seemingly physical reason" to obtain the equation of motion (= ex. Dirac equation ) and Hamiltonian (= total ) energy, both of which could be obtained from the common artificially-created Dirac or Klein-Gordon Lagrangians, by **imitating** (irrelevant) classical Lagrangian and Hamiltonian principle.

*(Fig.7) Euler-Lagrange → equation of motion ( potential energy is gone ? )*

In the original classical mechanics, when the action S is invariant under some coordinate transformation, Lagrangian gives the equation of motions through **Euler-Lagrange** equation.

↑ This original equation of motion based on authentic Lagrangian including potential energy (= V ) is described as the particle's acceleration (= mass m × second time derivative of x ) equal to the space derivative of external potential energy ( this p.2, this p.2 ).

On the other hand, all Einstein relativistic energy-momentum equation, which is the basis of Klein-Gordon and Dirac equation, has No potential energy (= because of free particle ), hence, relativistic quantum field theory used the completely-**different** cencepts called "rest mass energy (= mc^{2} )" as a (fake) **substitute** for external potential energy, which is illegitimate, Not the true Lagrangian.

Furthermore, the original classical Euler-Lagrange equation contains only the time derivative (= overdot-x, this-(6.3) ), but the (fake) modified Euler-Lagrange equation of relativistic quantum field theory contains both time and space (= x,y,z ) derivatives ( this p.7, this (1.5) )

Fabricating the fake new "relativistic" Lagrangian (= L ) → Using the fake modified Euler-Lagrange equation to get relativistic energy-momentum relation of quantum field theory such as Dirac and Klein-Gordon equations. ← This meanigless manipulation is what the relativistic quantum field theory is doing.

The original classical Euler-Lagrange equation gives the relation of the particle's **acceleration** equal to the external force (= the space derivative of potential energy, this p.2 ).

But the **fake** modified relativistic Euler-Lagrange equation gives the "free energies" (= **Not** acceleration or force, ← this unit is different from the original Euler-Lagrange equation ! ) of free particles ( this p.10-13 ), which completely **contradicts** the original Euler-Lagrange equations.

*(Fig.8) Lagrangian (= L ) → ( fake ) momentum (= p or π ) → Hamiltonian energy (= H ) containing unreal infinite (virtual) particles. = relativistic quantum field theory such as Dirac and Klein-Gordon (= K-G ) equations*

In the real (= classical ) physics, the particle's momentum (= p = mv, m is mass, v is velocity equal to the time derivative of the space coordinate x or denoted by overdot-x ) and Hamiltonian (= H = total energy ) can be obtained from (real) classical Lagrangian ( this p.3, this p.4, this p.14 ).

Relativistic quantum field theory uses the **fake** artificially-invented Lagrangian, so their momentums obtained by applying the normal classical procedure to fake relativistic Lagrangians are Not true momentums.

The real momentum p is expressed as m × v (= m is the particle's mass and v is velocity or the time derivative of x, where overdot-x means the time derivative of x = dx/dt ).

The relativistic Klein-Gordon (= K-G ) fake momentum (= π ) becomes just the time derivative of K-G field (= overdot-φ ) **without** the mass m, which is not a real momentum description ( this p.4-lower, this p.3 ).

And the relativistic Dirac equation's fake momentum (= π ) contains **No** time or space derivatives, instead, it becomes just the complex conjugate of Dirac field (= denoted by ψ^{†}, which is nonphysical complex conjugate of transpose matrix of Dirac field of ψ, this p.24-last, this p.2-upper ).

This nonphysical Dirac's momentum ψ^{†} just flips the sign of the nonphysical imaginary number ( i → -i ) in the original Dirac field (= ψ ), which has **nothing** to do with real momentum expressed as mass × velocity ( this 4th-last paragraph ).

↑ These fake momentums used in relativistic quantum field theory are called "canonical momentum (= π )."

Using these fake momentums and copying the ordinary classical method of obtaining Hamiltonian ( this p.17, this p.2 ), the relativistic Klein-Gordon and Dirac equations try to obtain their fake Hamiltonians (= H = total energy ), which contain nonphysical infinite (virtual) particles expressed as abstract math symbols ( this p.41-45, this p.13-14, 23 ).

As I said, all these relativistic (virtual) particles must have unrealistic infinite energies and momentums to satisfy the strict relativistic Lorentz invariance or symmetry rule, which calculation results always diverge to infinity.

So all the relativistic quantum field theory, QED, standard model are completely **useless**, unreal, **irrelevant** to our real world phenomena.

In classical mechanics, the Lagrangian is defined using kinetic energy T and the potential energy V, as follows,

*(Eq.1-11)*

where "dot" means time derivative.

Lagrangian is an artificial tool for getting some equations of motion and the Hamiltonian energy (= Hamiltonian usually means the total energy = potential energy + kinetic energy in classical mechanics, but quantum field theory **broke** this rule ).

Lagrangian (= L ) or action (= S = integral of L ) itself has No physical meaning ( this p.1-last ) which ambiguous and **unphysical** nature of Lagrangian was **exploited** in another unphysical theory = quantum field theory to make it look like having some physical meaning by artificially creating fake Lagrangian, Hamiltonian energies by imitating and modifying the classical mechanics.

Relativistic quantum field theory and QED **deliberately changed** the original definition of Lagrangian to artificially adjust their **fake** Lagrangian to their phony relativistic theory

When we substitute the Lagrangian (L) of Eq.1-11 into the **Euler-Lagrange equation** of

*(Eq.1-12) Original classical Euler-Lagrange equation.*

We can get the *equation of motion*.

These original authentic Lagrangian and Euler-Lagrange equation are completely different from the (fake) Lagrangians used in relativistic quantum field theory such as Klein-Gordon and Dirac equations ( this p.10-13 ).

By the way, how can we get the above Euler-Lagrange equation ?

The time integral of the Lagrangian is called the **action** denoted by **S**.

*(Eq.1-13)*

Originally, this action and Lagrangian themselves have No physical meaning ( this p.1-last ).

But at least in classical mechanics, this Lagrangian is based on experimental results. It's surprising and **unreasonable** that the relativistic quantum field theory artificially modified the original definition of these experimentally-verified classical Lagrangian and action.

The relativistic quantum field theory artificially changed this definition and added the space variables (= x,y,z ) to this original time variable (= t ) in the action with No reasonable explanation, so relativistic Lagrangian lacks reality like unreal virtual particles.

When the action S is minimized, the first-order change of

*(Eq.1-14)*

must be **zero**.

Considering the changes of q (= space variable, x ) and the time derivative of q (= velocity ), Eq.1-14 is expressed as ( this p.6-9 )

*(Eq.1-15)*

where

*(Eq.1-16)*

where q is a generalized coordinate.

The endpoints ( t1 and t2 ) of the action are *fixed*, so Eq.1-16 becomes *zero*, as follows,

*(Eq.1-17)*

As a result, when the change of the action (= Eq.1-14 ) is zero, the following condition is satisfied.

*(Eq.1-18)*

Finally, we get **Euler-Lagrange** equation of

*(Eq.1-19)*

↑ This authentic classical Euler-Lagrange equation is completely different from the later-invented **fake** Euler-Lagrange equation of the relativistic quantum field theory.

In case of quantum field theory, we do variation with respect to some (nonphysical) field operator ( for example, φ ), as follows,

*(Eq.1-20)*

In Eq.1-20, physicists artificially changed the original classical Lagrangian and action, and use the derivatives of φ with respect to x^{μ} = ( ct, x, y, z ). ← Not only the time t in classical mechanics.

And like Eq.1-16 and Eq.1-17, the endpoints of the action are fixed ( δφ = 0 at a1 and a2 ), so total differential of the second line is zero.

Getting Hamiltonian through Legendre transform from Lagrangian is one of the most important ways in the relativistic quantum field theory (QFT), though the relativistic Hamiltonian and momentum obtained by this procedure lack reality, and disagreeing with the original authentic classical Hamiltonian and momentum.

In Lagrangian, the **canonical** ( or generalized ) momentum (= p ) is defined as

*(Eq.1-21)*

**Hamiltonian** (= H = total energy ) is expressed as the Legendre transform of the Lagrangian, as follows,

*(Eq.1-22)*

When Lagrangian is Eq.1-11 (= classical ), Hamiltonian becomes

*(Eq.1-23)*

So we get the classical Hamiltonian (= total energy E = kinetic + potential energies, this p.2 ) of

*(Eq.1-24)*

*(Fig.9) classical Lorentz magnetic force causes unphysical QED interaction term (= ψAψ ) consisting of unreal virtual photons (= A ) and electrons (= ψ ) ?*

All the unphysical relativistic quantum field theories, QED and standard model rely on **unreal** virtual particles and virtual photons as **imaginary** mediators of forces or interactions between particles such as electrons.

Relativistic quantum field theory tries to obtain the fictional interaction term (= exressed as abstract Feynman diagram, this p.3-6 ) between the (virtual) photons allegedly contained in magnetic vector or electric scalar potential (= A, this p.5-8, this p.2-right-lower ) and electrons allegedly contained in nonphysical Dirac wavefunctions, from the ordinary classical Maxwell equation and Lorentz force law by artificially creating the fictitious Lagrangian and using wrong math.

Relativistic quantum field theory can only describe all these fictitious (virtual) photons and electrons as the abstract **nonphysical** math symbols (= a photon is expressed just as a meaningless symbol a^{†}, this p.3 ) with **No** concrete figure, which tell us **nothing** about the detailed mechanism of how each electron interacts with a (unreal virtual) photon ( this p.149-151 ).

Here, we show the artificially-created fictitious Lagrangian allegedly giving the fictitious interaction between (virtual) photons and electrons ( this p.3 ) is based on **wrong** math and physics, so wrong.

*(Fig.10) Create artificial Lagrangian → Euler-Lagrange equation → using wrong math → electromagnatic Lorentz force → (unreal) virtual photons in QED*

Originally, Lagrangian (= L ) has **No** physical meaning ( this p.1-last ).

Unphysical quantum mechanics **exploited** this unreality and **ambiguity** of Lagrangian, and tried to invent various **fictitious** Lagrangians for relativistic quantum field theory, QED and standard model.

Using one of these fictitious Lagrangian, they tried to obtain (= **mimic** ) the ordinary electromagnetic Lorentz force relation through Euler-Lagrange relation, using the **wrong** math trick ( this middle, this-6.1.18-6.1.19, this p.2-(9) ).

And using this fictitious Lagrangian, they tried to obtain fictitious Hamiltonian (= energy ) allegedly including the fictitious interaction term between ( unreal virtual ) photon expressed as magnetic vector potential A and an electron ( this p.5-6, this p.18-22 ).

↑ We prove this calculation of allegedly getting Hamiltonian energy used for QED is based on wrong math, so QED is illegitimate.

When the charge ( e > 0 ) is moving in the external electric (E) and magnetic field (B), the **equation of motion** (= Lorentz force ) is

*(Eq.2-1) Ordinary Lorentz electromagnetic force*

This force is called "**Lorentz force**".

Here we use "four-vector potential (= this vector potential is an invisible fictitious potential introduced only for nonphysical theoretical calculations )" like current density, as follows,

*(Eq.2-2)*

In Eq.2-2, "A" is vector (magnetic) potential allegedly used for expressing the magnetic field B, and "φ" is *scalar (electric) potential* allegedly used for expressing the electric field E.

"Four-vector" means they transform like spacetime ( ct, x, y, z ) under Lorentz transformation (= Einstein insisted the electromagnetic field magically changed depending on observers' motions, which relativistic theory causes serious paradoxes, so wrong ).

*(Eq.2-2') Unreal Lorentz transformation of electromagnetic field.*

Using these (fictitious, invisible) magnetic vector (= A ) and electric scalar (= ψ ) potential, the electric (E) and magnetic (B) fields of Maxwell electromagnetic theory can be expressed as

*(Eq.2-3)*

*(Eq.2-4)*

These "**artificial**" definitions were indispensable for relativity and Maxwell equation.

( Frankly speaking, this artificial vector potential "A" itself was necessary only **for** unphysical special relativity or relativistic quantum field theory, QED. )

The fictitious **Lagrangian**, which leads to Lorentz force relaton of Eq.2-1 through Euler-Lagrange equation, is known to be

*(Eq.2-5) Fictitious Lagrangian for Lorentz force*

In Eq.2-5, "e" and "m" are the electron's charge and mass.

the overdot-x means the electron's velocity (= v ) or the time derivative of the electron's coordinate (= dx/dt = v = overdot-x ).

External magnetic (= A ) and electric (= φ ) vector potentials allegedly generate the external megnetic (= B ) and electric fields (= E ).

First we consider only the x (= **1** ) component of motion.

Substituting L of Eq.2-5 into Euler-Lagrange equation of Eq.1-19,

*(Eq.1-19) Here q is "x", overdot-q = dx/dt = velocity*

The first term of Eq.1-19 using artificially-introduced Lagrangian is

*(Eq.2-6)*

And the second term of Euler-Lagrange equation of Eq.1-19 is

*(Eq.2-7)*

Next, they blatantly used the **wrong** math in the time derivative of the magnetic vector potential (= dA/dt ) like

*(Eq.2-8) Wrong math trick; time derivative of external magnetic vector potential (= dA/dt ) spawns four fictitious time and space derivatives of A (= dA/dx, dA/dy ..) and the irrelevant electron's velocity (= dx/dt )*

In Euler-Lagrange equation (= Eq.2-8 ) of fictitiously-introduced Lagrangian, they generate four **fictitious** terms from one term of the time derivative of the magnetic vector potential (= this one term dA/dt allegedly generates **fictitious** four terms of partial derivatives = ∂A/∂t + ∂A/∂x + ∂A/∂y + ∂A/∂z ! this p.3-(15), this p.2-(9), this p.14-middle ), which is illegitimate and it is clear that physicists intentionally use this **wrong** calculation only for developing **unreal** relativistic quantum field theory or QED.

Because this time derivative of **external** magnetic vector potential (= dA/dt ) generates the irrelevant moving electron (= overdot-x = dx/dt = velocity v in above figure means the moving electron ), which is just a **wrong** math ( this middle, this p.3-middle, this p.1, this p.19-(196), this p.3-(18), this-(6) ).

↑ The external magnetic field or vector potential A magically spawned the electron (= overdot-x ) from the inside !? ← Impossible !

For example, when a charged particle or electron is moving in the **static** external magnetic field (= B = ∇ × A ), the time derivative of this **static** external magnetic potential A must be **zero**, which cannot give the terms (= all terms become zero in the static magnetic field ) used in the final Lorentz magnetic force relation from this artificial Lagrangian. ← paradox, and wrong math trick !

From Eq.2-6 and Eq.2-8, Euler-Lagrange equation of Lorentz force becomes

*(Eq.2-9) Euler-Lagrange equation of fictitious Lagrangian → time derivative of external magnetic vector potential (= dA/dt ) generates the fictitious moving electron (= dx/dt or overdot-x ) → Lorentz force ? ← wrong math trick !*

Using this relation, Eq.2-9 means the ordinary Lorentz force of Maxwell equation, they claim.

*(Eq.2-10)*

But as shown in Eq.2-8 and Eq.2-9, this procedure of artificially getting Lorentz foce relation is **illegitimate** and based on **wrong** math.

Because they intentionally try to generate the (fictitious) **moving electron** (= expressed as the time derivative of electron's coordinate = dx/dt or overdo-x ) from the irrelevant time derivative of external magnetic vector potential (= dA/dt magically generates dx/dt or moving electron ? ) ← Impossible !

For example, in the **static** and constant external electro-magnetic field (= magnetic vector potential A is constant irrespective of the time t ) where the time derivative of magnetic vector potential A always becomes zero (= dA/dt = 0 ) in Eq.2-8, the moving electron's term (= dx/dt ) **disappears** and this fictitious Lagrangian cannot express Lorentz force.

Originally, the external magnetic (or electric ) vector potential (= A ) should be a function of the space variables (= x, y, z ) which space variables are **independent** of the time variable t (= space variables x,y,z of the magnetic potential are Not functions of time t ), so the splitting dA/dt into four partial time derivative terms like in Eq.2-8 and Eq.2-9 is a **wrong** calculation.

As seen here, the nonphysical quantum field theory tries to exploit and artificially manipulate the nonphysical Lagrangian to get the seeming physical equation even by using the wrong illegitimate math, so the quantum field theory lacks reality.

Using Eq.1-21, the (fictitious) momentum (= p, this p.6 ) obtained from this fictitious Lagrangian is

*(Eq.2-11)*

This is equal to Eq.2-7.

From Eq.1-22, Hamiltonian energy (= H ) of Lorentz force is ( this-6.1.13-6.1.16 )

*(Eq.2-12)*

So the magnetic force (= vector potential A ) doesn't contribute to the total energy.

And the momentum of Eq.2-12 can be expressed using the (fictitious) canonical momentum of Eq.2-11, as follows,

*(Eq.2-13)*

The canonical momentum p of Eq.2-13 is a fictitious (= **unreal** ) momentum created from the fictitious Lagrangian, but relativistic quantum field theory and QED try to use this fictitious momentum p as an electron's momentum expressed as de Broglie wave derivative ( this middle ), like

*(Eq.2-14) Fictitious Hamiltonian including unreal virtual photon A.*

From the fictitious Hamiltonian energy (= H, this p.3, this p.19 ) obtained from fictitious Lagrangian and momentum, physicists claim Eq.2-14 represents the (fictitious) interaction between electrons expressed as nonphysical Dirac field and (unreal virtual) photon field (= A ) in QED ( this p.10, this p.3, this last, this p.3, this p.3-left ).

But as shown in this, this calculation is based on completely **wrong** math trick, so there is **No** legitimate theory backing this phony QED interaction.

*(Fig.11) Artificial Lagrangian → Euler-Lagrange equation → Maxwell equation ? but → unreal Hamiltonian energy ← this unreal Hamiltonian is used in relativistic quantum field theory and QED = a wrong theory.*

Relativistic quantum field theory and QED try to artificially create **fake** Langrangian for classical Lorentz force law using the **wrong** math trick.

They try to create another **fake** Lagrangian for relativistic Maxwell electromagnetic theory.

Originally, Lagrangian itself has No physical meaning. Quantum field theory exploits the nonphysical nature of Lagrangian as a source of (fictitious) relativistic equations and Hamiltonian energies, by creating various forms of artificial Lagrangians seemingly imitating classical Lagrangian.

Quantum field theory claims this fake Lagrangian (= Fig.11 ) gives Maxwell equation by putting this Lagrangian into ( quantumg field theory version's ) Euler-Lagrange equation.

But unfortunately, this fake electromagnetic Lagrangian gives the wrong **unreal** Hamiltonian energy (= H = Hamiltonian energy should be the total energy summing kinetic and potential energies ) including nonphysical **unreal** energy term of "**JA** (= "A" is unseen fictitious magnetic vector potential, J is electric current )" by imitating the standard procedure for getting Hamiltonian (= H ).

Here we confirm this calculation for getting (unreal) Hamiltonian energy (= H ), and prove the relativistic quantum field theory and QED are based on this wrong unreal electromagnetic theory or fictitious Lagrangian potential energy (= JA ).

First we define the new concept of antisymmetric tensor ( **F _{μ ν}**, this p.4 ) used for artificial Lagrangian, as follows,

In Eq.3-1, the symbol "A" means the (fictitious) magnetic vector (and electric scalar) potential.

**Lagrangian** for Maxwell's equations can be defined as

*(Eq.3-2) Fictitious Lagrangian for Maxwell electromagnetic theory*

where μ_{0} means vacuum permeability.

As I said above, we need to sum up *0, 1, 2, and 3 components (= 0 is time t, 1,2,3 are space x,y,z components )* in both μ and ν, because both those variables are used twice in one term ( In this site, we use -1,1,1,1 version of metric tensor, you can freely change this metric tensor and sign using this ).

*(Fig.11') Artificial and fictitious relativistic electromagnetic Lagrangian-2.*

First, we use the standard procedure for getting Hamiltonian energy (= H ) from this fictitious electromagnetic Lagrangian, and prove this Hamiltonian is **unreal**, so relativistic quantum field theory and QED are wrong.

We insert this artificially-created relativistic Maxwell's Lagrangian into the standard relation (= quantum field theory's version ) for getting Hamiltonian energy (= H ).

Generalized (= canonical) momentum (= p ) of this whole system obtained by the standard method from this Lagrangian is a completely unreal meaningless momentum (= with No physical meaning ) expressed as the "electric field E ( this p.2-third-sentence, this p.11-(59) )."

And Hamiltonian energy (= H, which should be equal to the total energy ) obtained from this Lagrangian becomes completely different from the ordinary real Maxwell equation's electromagnetic energy.

↑ True electromagnetic energy ( density ) should take the form of 1/2( εE^{2} + 1/μ B^{2} ) where E and B are electric and magnetic field, respectively.

But this fictitious Lagrangian (= L ) gives the completely different and **fictional** Hamiltinian energy (= E ) including the "fictitious nonexistent potential energy" term expressed as J_{μ}A^{μ} where J_{μ} is the electric current or charge density ( this p.2 ), A^{μ} is the fictitious magnetic and electric vector potentials which must **Not** appear in the real electromagnetic (Hamiltonian H) energy ( this p.4-(23), this p.11-(61d) ).

Furthermore, the procedure for getting Hamiltonian uses the time derivative of the magnetic vector potential A (= dA/dt or overdot A ), which breaks the normal symmetric electromagnetic field energy (= the symmetric form of E^{2} + B^{2} is broken, because dA/dt or ∂A/∂_{0}A modifies only the electric field E, while the magnetic field B or space derivative remains the same ).

Even if physicists manage to get the normal symmetric electromagnetic energy density = 1/2( εE^{2} + 1/μ B^{2} ), the unreal potential energy J_{μ}A^{μ} (= only the fictitious magnetic potential energy components μ = 1.2.3 remain, while the electric potential term = φρ vanishes, which is unreasonable ) remains in the final Hamiltonian energy ( this p.2-(5.13), this p.5-6 ).

↑ In order to avoid this unreal potential energy term (= J_{μ}A^{μ} ) in the final Hamiltonian, physicists tried to impose various **artificial rules** such as "free-field vacuum energy" where all electric (= φ ), magnetic vector potential (= A ) and the charge (= ρ ), current (= J ) densities should be zero (= JA = 0 ) from the beginning ( this p.15-lower-p.16, this-lower ). ← But if these fictitious magnetic vector potentials and the electric current J are zero, the ordinary Maxwell equations cannot be obtained from this fictitious Lagrangian through Euler-Lagrange equation ( this p.2,5 this p.12-13, this p.3-4 ).

This result of unreal Hamiltonian energy clearly shows all the relativistic quantum field theory, QED and standard model based on this artificially-created fictitious electromagnetic Lagrangian are **false**.

Next, we actually get Maxwell equation from this fictitious Lagrangian (= this fictitious Lagrangian was artificially created only for getting Maxwell equation, but it **failed** to give real Maxwell electromagnetic (Hamiltonian) energies, hence illegitimate Lagrangian, after all ).

When we substitute Lagrangian of Eq.3-2 into the following Euler-Lagrange equation ( see also Eq.1-20 ), we get the usual **Maxwell equations** in the form of vector potentials.

*(Eq.3-3)*

We can get the usual Maxwell's equation.

( Replacing E and B fields by A and φ, this proves to be usual Maxwell equation, this p.14 )

Here we explain about the detailed calculation method of Eq.3-3.

In case of μ=1, using Lagrangian of Eq.3-2, the first term of Euler-Lagrange equation of Eq.3-3 is

*(Eq.3-4)*

The differentiation with respect to A^{1} acts only on the second term.

And we think about the case of ν = 2 ( μ = 1 ) in Eq.3-3.

In this case, two terms including F_{12} or F_{21} are related.

In this site, we use the metric of (-1,+1,+1,+1) version.

So the second term of Euler-Lagrange equation of Eq.3-3 is

*(Eq.3-5)*

where we use

*(Eq.3-6)*

As shown in Eq.1-1 and Eq.1-8, the sign of 1,2,3 (= x,y,z ) component does not change depending on the index position ( upper or lower ).

We should worry only about the zero componet about the index position.

For example, when μ = 1 and ν = 0, terms including F_{10} and F_{01} are involved, so the second term of Eq.3-3 becomes

*(Eq.3-7)*

where we use

*(Eq.3-8)*

The sign of Eq.3-8 is opposite to the result of Eq.3-5.

But considering Eq.3-8, the final derivative becomes the same form as Eq.3-3,

*(Eq.3-9)*

As a result, in all cases we obtain the **same form** of Maxwell equation.

According to Eq.2-4, the magnetic field *B* can be expressed, as follows, (using F )

*(Eq.3-10)*

And according to Eq.2-3, the electric field *E* is

*(Eq.3-11)*

where *A ^{0} = - A_{0} = φ/c*. ( See Eq.2-2. )

( As I said above, these artificial definitions are to combine relativity and Maxwell equations. )

Replacing F_{μν} by elecrtomagnetic fields like Eq.3-10 and Eq.3-11, we can prove that Eq.3-3 means the usual Maxwell's equations ( this p.14 ).

For example, μ = 1 in Eq.3-3,

*(Eq.3-12)*

F_{11} is zero in Eq.3-1.

Due to this relation, Eq.3-12 is just equal to Maxwell equation of

*(Eq.3-13)*

In the same way, when μ = 0 ( using this relation ),

*(Eq.3-14)*

where J^{0} = -J_{0} = cρ_{e}. (See Eq.1-10).

This is also one of Maxwell equations.

Next we explain a little about the calculation process of Eq.3-3.

As I said, two Fs of Eq.3-2 means

*(Eq.3-15)*

In the case of

*(Eq.3-16)*

Differentiating Eq.3-2 (Eq.3-15) with respect to Eq.3-16,

*(Eq.3-17)*

Considering Eq.3-15, we also need to calculate

*(Eq.3-18)*

Summing Eq.3-17 and Eq.3-18, **1/4** value of Eq.3-2 vanishes in Eq.3-3.

When you deal with zero compoment, you need to care about the relation between the sign and index position.

*(Eq.4-1) Einstein relativistic energy (= E ) momentum (= p ) relation*

where p is momentum, E is energy, m is a electron's rest mass, c is light speed.

Eq.4-1 is Einstein relativistic relation of mass (= m ), energy (= E ) and momentum (= p ) of a free particle (= with No potential energy ) where mc^{2} ( c is light speed ) means the rest mass energy of a particle.

This famous Einstein relativistic relation causes serious paradoxes, so false.

We use (-1,1,1,1) version notation.

In the quantum mechanics and relativistic quantum field theory, the relativistic energy (E) and momentum (p) are replaced by the de Broglie relation operators like

*(Eq.4-2) de Broglie wave operator, E = energy or time derivative (= ∂t ), p = momentum or space derivative (= ∇ = ∂x, ∂y, ∂z = ∂ _{1}, ∂_{2}, ∂_{3} )*

where i is imaginary number,

ℏ = h/2π where h is Planck constant

The problem is all the relativistic quantum field theory, QED and standard model use this de Broglie wave operators as the particle's momentum, and the relativistic theory contradicts de Broglie wave interference. ← Quantum field theory and QED are **illegitimate**.

Using Eq.4-2, Eq.4-1 can be expressed as

*(Eq.4-3) Relativistic energy-momentum relation replacing momentum (= p ) energy (= E ) by space and time derivatives (= de Broglie wave theory ) → relativistic quantum field theory or Klein-Gordon equation representing Higgs boson*

where the time derivative ∂_{0} = - ∂^{0} and the space derivative ∂_{i} = ∂^{i}, i = 1(= x ), 2(= y ), 3(= z ).

Eq.4-3 is called Klein-Gordon equation, which is the 1st relativistic quantum field theory, which is said to express all the spin-0 (scalar) particles such as nonphysical Higgs boson and other unseen (virtual) particles.

The point is these relativistic wavefunctions (= φ ) have **No** physical meaning, because the relativistic quantum field wavefunction (= φ ) can**not** represent the normal particle's probability density ( this p.2-last, this p.2 ), unlike the the ordinary Schrödinger's probability wavefunction.

This relativistic Klein-Gordon's wavefunction (= φ ) has **unreal negative probabilities** ( this p.7, this p.7, this p.6-4th-paragraph ) of infinite numbers of fictitious (virtual) particles ( this p.6-second-paragraph ), which are expressed
as nonphysical math symbols (= each particle is expressed as nonphysical a^{†}, b^{†}.. this p.4 ), which can tell us **nothing** about the detailed mechanism of relativistic quantum field theory (= or a "particle" itself cannot be defined, this p.3-last ).

Furthermore, in order to satisfy the unrealistic Einstein relativity (= all phenomena and energies magically "look" the same as seen by any observers moving at arbitrary speeds ), all the relativistic quantum field theories and QED must have **infinite** numbers of ( virtual ) particles with all kinds of energies and momentums from minus **infinity** to plus infinity ( this p.5, this p.5-lower, this p.2-lower ).

So in the **unreal** relativistic quantum field theory and QED, even the lowest ground-state energy is unrealistically infinite ( this p.6 (or p.7) 3rd-paragraph, this p.21-22 ).

↑ These unreal infinite virtual energies always cause the calculation results of all quantum field theory and QED to **diverge** to meaningless **infinity**, which must be artificially canceled by the another artificially-manipulable (unseen) infinite electron's bare charge, mass (= free infinite parameters, this p.4-5, this 2nd-paragraph ) to obtain freely-adjustable finite values (= anomalous magnetic moment in QED ).

This ad-hoc illegitimate method of artificially removing infinity to obtain the seeming finite value is called "renormalization ( this p.9-10 )", which is mathematically wrong (= ∞ - ∞ = finite value ? ← wrong meaningless QED math ) and criticized even by founders as "hocus-pocus ( this 1st-paragraph )."

God particle Higgs boson is said to be expressed using this unrealistic Klein-Gordon equation ( this 3rd-last-paragraph, this p.2-introduction ).

So Higgs boson also lacks reality, Higgs is expressed as the spin-0 Klein-Gordon particle with unreal negative mass ( this p.9, this p.5-4th-paragraph ).

The relativistic energy-momentum relation such as Klein-Gordon equation has the second-order energy and momentum (= E^{2} = p^{2} + .. ), which cannot incorporate Coulomb potential energy ( this 13th-paragraph ), hence, gives wrong energy results ( this p.5-last-paragraph, this p.1-3rd-paragraph ).

Relativistic quantum field theory = Klein-Gordon equation completely **failed**, though it is still used as (imaginary) Higgs boson.

*(Fig.12) Relativistic quantum field theory = Klein-Gordon field is just a nonphysical math theory with No real particle's figure.*

All the ad-hoc quantum field theories such as Klein-Gordon equations and QED imitate and modify the original classical Lagrangian's theory (= Lagrangian itself has No physical meaning, they exploit this nonphysical property of Lagrangian to express the nonphysical quantum field theory ).

First, they aritificially created the **fictitious** relativistic Klein-Gordon's Lagrangian (= L ) to obtain Klein-Gordon equation through (relativistic version of) Euler-Lagrange equation.

And, using this fictitious Lagrangian, they obtained the unreal canonical momentum (= which is also the artificially-created fictional concept ) and Hamiltonian (= total ) energy (= H ) of Klein-Gordon equaiton, which contains infinite numbers of (virtual) spin-0 particles with No concrete physical figures ( this p.6-second-paragraph ).

*(Eq.4-4) relativistic Klein-Gordon field wavefunction φ filled with unphysical particles (= such as Higgs and virtual particles ) expressed as nonphysical symbols = a ^{†}.*

*(Eq.4-5) ω = angular frequency, p = momentum, k = wave number*

*(Eq.4-6) E = relativistic energy, m = mass, c = light speed*

Eq.4-6 is equal to the original relativistic energy-moemntum relation of Eq.4-1.

And as shown in Eq.4-4, in quantum field theory, one particle with momentum k is created (or annihilated ) in **all space** at the same time to keep unphysical relativistic Lorentz invariance (= Einstein relativity with No absolute space doesn't allow distinguishing different places, so the unrealistic relativistic quantum field theory cannot strictly distinguish or describe each different particle at different place ).

And Eq.4-4 contains **infinite** particles of **every** momentum and energy (from -∞ to + ∞) to satisfy the strict condition of Lorentz symmetry (= any observers moving at infinitely-different speeds must see the same physical results in Einstein paradoxical world ).

So the quantum field theory *doesn't mean the real world where real particles with concrete figures are moving around.*.

The virtual Klein-Gordon particle's solution of the above Eq.4-4 uses the coefficient of the square root of 1/2ω, which coefficient values can be freely changed, so meaningless values.

If we want to change this coefficient into other arbitrary values such as 1/2ω or 1/2E instead of the square root of it, we can **artificially** change the other equations' coefficients such as the (pseudo-)particles' commutation relation's coefficient from this Eq.4-19 (= not attached to 2E ) to this (= attached to 2E or 2ω, this p.2-(5),(7), this p.21-(3.6)-p.22-(3.13) ) to give the same Hamiltonian (= total ) energy.

↑ So the coefficients of these artificial relations can be **freely changed** for obtaining the desirable artificial relativistic Klein-Gordon's Hamiltonian (= total ) energy's form, which is Not a prediction of the theory, but just a artificial manipulation of coefficients.

As you know, the velocity of the wave is obtained from frequency f × wavelength λ ( v = fλ ).

So the velocity of this wavefunction becomes

*( Fig.T-1 )*

E is the huge relativistic energy consisting of the particle's momentum p and rest mass energy (= mc^{2}, this p.6 ), E = hf where h is Planck constant and f is (large relativsitic) frequency.

From de Broglie wave theory, the particle's wavelength λ = h/p where p is momentum, so the particle's velocity becomes v = fλ = E/h × h/p = E/p, which is faster than light ( > c this p.3 )

This unreasonable wavefunction is caused by the **relativistic invariance** of the equations.

Ironically, the relativistic restriction causes imaginary "tachyon".

They insist if we combine negative and positive energy solutions in Dirac equation, this tachyon vanishes.

But each electron or positron is **faster-than-light**. This is strange.

The equations from Eq.4-7 to Eq.4-11 ( complex scalar field ) are moved into this page.

*(Eq.4-11)*

where θ means "step function".

Eq.4-11 shows that by artificially adjusting coefficients, the relativsitic Klein-Gordon wave function can be expressed as the form of relativistic Lorentz invariance contaning the integration of d^{4}p (= or d^{4}k = four momentums ) instead of d^{3}p or d^{3}k, and the interval is from minus infinity to plus infinity to be Lorentz-invariant (= any observers moving at arbitrary speeds should see the same physical phenomena ), which causes serious **divergence** ( this p.5 ).

Artificially-created Lagrangian (= No physical meaning ) for getting Hamiltonian (= total ) energy of relativistic Klein-Gordon equation ( here, this notation is used ) is defined as

*(Eq.4-12) Artificially-created relativistic Klein-Gordon Lagrangian (= L )*

where "overdot" means time derivative,

φ is the relativistic Klein-Gordon wavefunctions containing infinite numbers of (virtual) spin-0 particles such as Higgs.

These relativistic (artificially-prepared) Lagrangians for relativistic free particles (= with No potential energies ) **contradict** the original definition of (classical) Lagrangian which should be expressed as L = T (= kinetic energy ) - V (= potential energy ).

↑ The artificially-created relativistic Lagrangian (= L ) unreasonably replaced the original (external) potential energy (= V ) with the **irrelevant** rest mass energy ( V → mc^{2}, this p.4 ), which replacement completely disagrees with the true Lagrangian which must contain the (external) potential energy V.

Substituting the artificially-created relativistic Lagrangian of Eq.4-12 into Euler-Lagrange equation of Eq.1-20, we get relativistic Klein-Gordon equation ( this p.3, this p.16, ).

*(Eq.4-13) Substituting the fictitious relativistic Lagrangian into Euler-Lagrange equation → Klein-Gordon equation *

From Eq.4-12 and definition of Eq.1-21, the fictional **canonical momentums** (= **Not** real momentum ) is

*(Eq.4-14) Relativistic Klein-Gordon (fake) generalized canonical momentum = π*

↑ This generalized (canonical) momentum of relativistic Klein-Gordon equation is the artificially-created imaginary concept, hence, **Not** a real momentum, due to its wrong math.

The real momentum (= p ) must be expressed as a particle's mass multiplied by its velocity (= p = mv, this-(2.3.7), this p.4-(6.20), this p.7 ).

This Klein-Gordon's ( fictional canonical ) momentum (= π ) is expressed just as the time derivative of the field (= dφ/dt or overdot-φ ), which does Not contain the mass (= m ) of the real momentum of mv, hence, completely a different and **fake** momentum !

By substituting the artificially-created Klein-Gordon Lagrangian (= L ) into Eq.1-22, the fictitious Hamiltonian (density) or total energy of Klein-Gordon field ( this p.4 ) is

*(Eq.4-15)*

Substituting the Klein-Gordon wavefunction φ of Eq.4-4 into Eq.4-15, and integrating it in all space, we can get the following final form of the fictitious relativistic Klein-Gordon's **Hamiltonian** energy ( this p.2~4, this p.13 ), using this calculation

*(Eq.4-16) Fictitious Klein-Gordon's Hamiltonian (= final form of H ) or total energy*

After all, the final form of Hamiltonian (= total ) energy (= H ) of the relativistic Klein-Gordon equation consists **only** of **unphysical** particle (= expressed just as abstract math symbols such as a or a^{†} ) with infinite kinds of energies and momentums (= integral over all momentums k from -∞ to +∞ ), which is just a nonphysical math theory clarifying **No** detailed physical mechanism ( this p.6-12, this p.4-5 ).

The nonphysical symbol " a^{†} " means the particle's creation operator (= increasing one particle ), and " a " means the particle's annihilation operator (= decreasing one particle ), which abstract operation is the only thing the useless quantum field theory can express as particles' motion.

In the process of obtaining this fictitious relativistic Klein-Gordon Hamiltonian (= total ) energy, the positive (unrealistic) infinite energy term (= Dirac delta function δ(0) = infinity ) appears due to the illogical quantum mechanical relation or rule ( this p.4-5, ).

Some physicists claim this (unphysical) vacuum positive infinite energy (= expressed as infinite delta function = +δ(0)) appearing in relativistic Klein-Gordon scalar-spin-0-particle total energy can be canceled out by another unrealistic negative infinite vacuum energy (= -δ(0) = -∞, which I explain later ) appearing in Dirac spin-1/2-particle's Hamiltonian energy using the hypothetical nonphysical theory called "supersymmetry ( this p.23, this p.7, this p.13 )" or ad-hoc renormalization artificially removing infinity ( this p.23, this p.26 ).

↑ But both relativistic Klein-Gordon's spinless particle (= bosons ) and Dirac's spin-1/2 particle (= fermions ) are free particles ( this p.2 ) with No potential energies, which cannot be negative energies (= free particles with positive kinetic energy and No negative potential energy must always have zero or positive total energies ), so the ficititious negative infinite energy canceling
positive infinite energy between free spin-0 and spin-1/2 particles stated by the imaginary supersymmetry is **unrealistic** and wrong.

Here we explain about the detailed calculation of the upper Klein-Gordon's Hamiltonian.

We substitute the fictitious Klein-Gordon's wavefunction of Eq.4-4 into φ^{2} of Eq.4-15 (= Klein-Gordon Hamiltonian energy equation ).

Each momentum k or k' ( from -∞ to +∞ ) is independently integrated from each other in the two φ^{2}.

So we use

*(Eq.4-17)*

Using Eq.4-17, φ^{2} of Eq.4-15 becomes

*(Eq.4-18)*

The terms of a^{†}a^{†} (= particle creation-creation ) and aa (= particle annihilation-annihilation ) in the upper equation are zero due to the zero coefficient of the final Hamiltonian energy, so they are eliminated.

Here we use

*(Eq.4-19) Artificial rule of Klein-Gordon's particles.*

The rule of the upper Eq.4-19 is the artificially-created **commutation** rule imposed on fictitious Klein-Gordon or spin-0 scalar bosons ( this-middle, this p.3, this-(7) ).

The artificial rule of Eq.4-19 means the interchange of the (nonphysical) particle creation operator (= a^{†} ) and annihilation operator (= a ) gives the meaningless infinity as delta function δ(k-k') where this delta δ function becomes infinity when these two momentums are equal (= k-k' = 0 ), or this delta function becomes zero when k is not equal to k'.

The notation about the above commutation relation of (unphysical) particles is like in this p.1-lower, this-(8.2.10).

↑ Dirac's delta function (= δ(k-k') which could be infinity, when k = k' ) has to be used in the relativistic quantum field theory which must contain all kinds of momentums (= k ) **continuously** from minus infinity to plus infinity, which is why QED results always diverge to meaningless infinity ( this p.22 ).

In the last line in Eq.4-18, we exchange k and k' of one term, and unite it with another.

Integrating Eq.4-18 ( first term ) with respect to space variables, we obtain

*(Eq.4-20)*

where delta function's formula is used.

From the definition of Eq.4-5,

*(Eq.4-21)*

Using Eq.4-15, Eq.4-20 and Eq.4-21, the final form of (fictitious) Hamiltonian becomes

*(Eq.4-22) Fictitous Klein Gordon Hamiltonian (= H ) final form*

The final form of this upper Hamiltonian (= H should be total energy E or ℏω ) is **Not** a true Hamiltonian, because this fake Klein-Gordon's Hamiltonian originally gives **twice** the total energy (= 2E^{2} = 2(ℏω)^{2} instead of the true Hmiltonian energy = E, as shown in the upper Eq.4-22 last line ) and this the wrong total energy (= 2(ℏω)^{2} ) value is **artificially canceled** out by the coefficient **parameter** (= 1/**2**ω = this parameter "**2**" can be artificially changed into other values ) inserted in the artificially-created Klein-Gordon's wavefunction (= φ, this p.7-9, this p.15 ) in advance.

In the second line from the last in Eq.4-22, we use the relation ( this-(A-45) ) of

*(Eq.4-6)*

As a result, adding delta function of Eq.4-18, we get the final version of fictitious relativistic Klein-Gordon Hamiltonian of

*(Eq.4-23)*

Fictitious relativistic Klein-Gordon Hamiltonian energy includes infinite vacuum energy (= delta function δ(0) = +∞ ).

When the relations of Eq.4-19 is satisfied, Eq.4-4 and their **fictional** *canonical momentums* (= π ) in Eq.4-14 satisfy the **commutation** relations of

*(Eq.4-24)*

Eq.4-24 can be confirmed by a little long calculations ( this p.13-17 ).

As you know, the famous commutation relation of Eq.4-24 is based on **de Broglie's relation** ( quantum mechanical momentum p is expressed as the space derivative ) of

*(Eq.4-25) original quantum mechanical commutator relation deos Not contain infinite delta function.*

Relativistic Klein-Gordon's fictional canonical momentum (= π ) is Not a real momentum, so blindly applying (and modifying ) the original quantum mechanical commutation rule (= Not including infinite delta function ) between the space coordinate (= q ) and the momentum (= de Broglie wave operator ) to this fictional Klein-Gordon momentum is **baseless**.

In this section, we explain violation of relativistic causality briefly.

Basically the propagator contains the *two processes* of particle and antiparticle.

If we consider the propagator of **only** particle ,

*(Eq.4-26)*

Suppose t = t'.

If Eq.4-26 doesn't include **ω _{k}** as a coefficeint, Eq.4-26 becomes

Eq.4-27 means that when x is different from x', Eq.4-27 is zero.

So Eq.4-27 satisfies

But Eq.4-26 includes ω_{k} as a coefficeint.

So the calculation result of Eq.4-26 is

*(Eq.4-28)*

Eq.4-28 is **NOT** zero in the *space-like* region of

*(Eq.4-29)*

So according to the relativistic quantum field theory (QFT), the particles can be faster than light ( this p.3 ), even though they use the special relativisty !

This is clearly **self-contradiction**.

But if we combine *both* directions (= particle and antiparticle ) at the same time, this satisfies causality.

So the quantum mechanical physicists are satisfied with these results.

( How do you think about it ? )

Klein-Grodron fields express *π - meson* and *Higgs* particle.

As you notice, there are **no** concrete images in these particles.

*(Fig.D) Relativistic quantum field theory represented by Dirac equation contains unphysical γ matrices and the paradoxical energies contradicting Einstein relativistic energy-momentum relation, so Dirac fermions don't exist.*

Relativistic Dirac equation is the most important equation constituting the quantum field theory and QED (= quantum electrodynamics ) allegedly describing all spin-1/2 particles such as electrons, antiparticles, unseen quarks, neutrinos.. ( this 2nd-paragraph, this p.2 ) as nonphysical math symbols with No concrete figure. ← So relativistic quantum field theory and QED **lack** reality.

Relativistic Dirac equation is said to be a square root of Einstein's relativistic energy-momentum relation equal to the failed Klein-Gordon equation (= Dirac equation = square root of relativistic E^{2} = (pc)^{2} + m^{2}c^{4}, where E is relativistic energy, p is relativistic momentum, mc^{2} is rest mass energy, E, p are denoted by time and spatial differential operators based on de Brolgie wave theory in quantum field theory, this p.1-2 ).

But the square root of the original relativistic mass relation consisting of the second-order energy and momentum is **mathematically impossible** as seen in the failed Klein-Gordon equation.

So relativistic Dirac equation had to rely on some "**cheating**" which artificially divided the second-order relativistic energy-momentum relation into two **different** energy equations (= ① and ② in the upper Fig.D ) using nonphysical γ matrix ( this p.22-23, this p.29-30, this p.12-13 ).

The fact that relativistic Dirac equation can**not** describe any particles **without** the nonphysical γ matrices (= Dirac equation can**not** describe each particle using the ordinary numbers without matrices ) means all the current relativistic quantum field theory, QED and particle physics heavily relying on this nonphysical Dirac equation **lack** reality.

Relativistic Dirac equation's nonphysical γ matrices consist of Pauli σ spin matrices, hence, physicists claim this relativistic Dirac equation could successfully express electron's "spin ( this p.8 )" without showing any detailed mechanism or figure of this (illlusory) spin.

But actually, these Pauli spin σ matrices included in relativistic Dirac γ matrices have nothing to do with "spin", shwoing quantum spin is illusion.

The problem is these two relativistic (pseudo-)equations using nonphysical γ matrices or the alleged (pseudo-)square root of the original relativistic energy relation give **two types** of the completely different energy-momentum relations ( this p.3 ), one of which **contradicts** the original Einstein relativistic energy-momentum relation.

① of the upper Fig.D gives the normal relativistic energy E, which is approximately equal to E = pc + mc^{2} (← energy E, momentum p and the rest mass energy mc^{2} have the **same** sign ).

But ② of the upper Fig.D gives the **wrong** energy E, which is equal to E = pc - mc^{2} (= total relativistic energy E and momentum p have the opposite sign from the rest mass energy mc^{2} ), which **contradicts** the original Einstein relativistic energy relation where the relativistic total energy E must be the **sum** of momentum p and rest mass energy mc^{2}. ← Dirac's (pseudo-)square root of original Einstein relativistic relation **contradicts** the relativity !

Relativistic Dirac wavefunction consists of infinite numbers of (virtual) particles (= c^{†} ) such as electrons, quarks, and antiparticles like positrons ( = d^{†} ) expressed as the nonphysical abstract math symbols with No concrete particle's description ( this p.7, this p.6-second-paragraph ).

These Dirac's nonphysical particles such as electrons (= c or u ) have the upper ① energy relation, and antiparticles such as positrons ( d or v, this p.12-13 ) have the upper contradictory ② energy relation ( this p.16, this p.19, this last ), which fact proves relativistic Dirac equation is a **failed** wrong theory (← only the antiparticles must have the positive energy E and momentum p with paradoxical **negative rest mass** energy, like the upper ② ).

And like all other relativistic quantum field theory, Dirac equation must consist of infinite numbers of (virtual) particles and antiparticles with infinite amount of energies, which cause QED calculation results to **diverge** to **meaningless** infinity ( this p.4-6 ), which must be artificially canceled by another artificial infinity (= free parameters, this p.4-5 ) by the illegitimate method called "renormalization ( this p.13-14, this p.15-16 )" which wrong-math renormalization (= ∞ - ∞ = finite value ? ← infinity is Not a definite value, so this QED calculation is **Not** the prediction of the definite physical values at all ) was criticized even by founders such as Dirac himself ( this 1st-paragraph ) and Feynman.

So all the relativistic quantum field theory, QED and standard model based on the artificial manipulation of the meaningless infinite parameters ( this p.2-3, this p.3, this p.11-13 ) have **No** power to predict any physical values ( this p.36, this p.8 ), contrary to the media false narrative. ← Actually, Nobody uses this useless QED in our daily lives.

The point is the media and academia just repeatedly and **baselessly** say the tired cliche "successful QED predicting anomalous magnetic moment !", but they **Never** explain those "dubiously successful" calculation process of how to obtain such tiny finite physical values (= anomalous magnetic moment, this p.10-13 ) from the meaningless **infinity** which is the original QED calculation result ( this p.7 ).

Various artificial notations are used in quantum field theory.

On this page, (-1,+1,+1,+1) version of metric tensor is used.

*(Fig.13) Aritificially create fictitious Dirac Lagrangian (= L ) → Euler-Lagrange equation → Dirac equation. → fictional canonical momentum → fictional Dirac Hamiltonian energy (= H ) consisting of infinite (virtual) fermions and antiparticles. ← This meaningless concept is what the relativistic quantum field theory is.*

Like other nonphysical relativistic quantum field theory and QED, first, physicists artificially created fake Dirac's Lagrangian (= L ) including unphysical Dirac wavefunction and its adjoint (× γ^{0} matrix ) form filled with infinite free relativistic (unphysical) particles (= c or b ) and antiparticles (= d, this p1~2 ) with No potential energy which contradicts the original authentic Lagrangian consisting of kinetic and potential (= V ) energies.

Next, by imitating classical Lagrangian, inserting this artificially-created Dirac Lagrangian into Euler-Lagrange equation gives the Dirac equation (= which means this fictitious Lagrangian was created and chosen to give Dirac equation ).

Then, again, by imitating and modifying the classical momentum (= p = mv ) and Hamiltonian energy (= H ), they obtain the **fictional** (= canonical ) momentum (= π ) and fictional relativistic Dirac Hamiltonian (= total ) energy (= H, this p.3-5 ).

↑ This final form of relativistic Dirac Hamiltonian (= total ) energy consists of infinite numbers of nonphysical math particles ( this p.2-5 ) with unrealistic **infinite** energies ( this p.6, this p.23-second-paragraph, this p.98-102 ) with no physical shapes, which relativistic quantum field theory **lacking** realistic particle pictures can**not** be used for practical science at all.

In the upper figure, the nonphysical math symbols such as c^{†} and c mean the electron or particle's creation and annihilation operators, and d^{†} and d mean the antiparticle's creation and annihilation oeprators, respectively ( using other letters such as a and b instead of c and d as particles or antiparticles is OK ).

u(k) and v(k) are the unphysical 4×1 matrices.

u^{†}(k) (= or bar-u(k) ) and v^{†}(k) (= or bar-v(k) ) are 1×4 matrices.

All calculations of relativistic quantum field theory, QED and particle physics with these unrealistic infinite (virtual) particles' energies are known to give only unrealistic divergence or meaningless **infinities**, which must be artificially removed by the ad-hoc renormalization ( this 3rd-paragraph ) using freely-adjustable-infinite-parameters ( this p.62-72 ), which is useless, cannot predict any physical values (= physicists cannot define or predict the value of indefinite "infinity" to cancel the original QED infinity ), contrary to the media-hype.

↑ So all calculations (= giving only meaningless infinities ) in the current relativistic quantum field theory based on Dirac and Klein-Gordon equations are physically **meaningless** and useless.

The artificial notation of bar-ψ in the above Lagrangian means the complex conjugate transpose or adjoint Dirac wavefunction (= ψ^{†}, this p.8 ) times unphysical γ^{0} matrix.

↑ This **artificial** ad-hoc notation is necessary in (pseudo-)relativistic Dirac equation, because the nonphysical 4×4 γ^{j} matrices (= j = 1,2,3 components ) are anti-Hermitian or Not Hermitian (= complex conjugate transpose of γ^{j} matrices γ^{j †} are Not equal to the original γ^{j} matrices, this p.2-lower-p.3-upper, this p.3-(75) ). ← This meaningless math is a serious problem for quantum field theory, and add the ad-hoc γ^{0} matrix to Dirac equation is necessary for producing the adjoint form.

So the γ matrices allegedly representing 4×4 matrix-spin are completely different from 2×2 Pauli matrices (= the complex conjugate transpose of Pauli matrices are equal to the original Pauli matrices like σ^{†} = σ = Hermitian, this-(2.4.12) ), but they try to associate this γ matrix to irrelevant "spin" allegedly expressed by Pauli spin σ matrix.

Anyway, there is **No** physical reality in particles and antiparticles allegedly expressed by the current relativistic quantum field theory.

*(Eq.5-1) Nonphysical relativistic Dirac equation cannot describe real particles !*

Nonphysical relativistic Dirac equation is expressed as Eq.5-1
where ψ(x) is the 4-component Dirac particle's wavefunction (4 × 1 matrix), γ^{μ} is 4 × 4 matrix, whose particles and antiparticles are just a nonphysical math with **No** concrete physical picture ( this p.2, this p.7 ).

Here we use (-1,+1,+1,+1) version of metric tensor (= only zero component or time variable ct = x^{0} = -x_{0} changes its sign between subscript and superscript, while space variables = x,y,z or 1,2,3 components do not change their signs in any index positions x^{1} = x_{1} ), so if you want to convert it into the other version, see this page.

In quantum field theory, the energy (= E ) and momentum (= p ) are expressed using the time and space derivatives (= de Broglie relation ), so Eq.5-1 is equal to

*(Eq.5-2) Relativistic Dirac equation expressing energy (= E ) and momentum (= p ) by the time and space derivatives (= ∂ )*

The upper Eq.5-2 uses (-1,+1,+1,+1) version of metric tensor, so this expression has the different sign from this (+1,-1,-1,-1) version of notation.

Various artificial notations are often used in quantum field theory.

Dirac equation of Eq.5-2 must satisfy the 1st-failed relativistic Klein-Gordon equation (= second-order energy and momentum which are closer to the original Einstein relativistic relation ) to be equal to special relativity.

In order to obtain the Einstein relativistic equation and the 1st-failed relativistic Klein-Gordon equation, we need to add the following equation containing the energy (= E = cp^{0} ), momentum (= p^{i}, i = 1,2,3 ), nonphysical γ matrices, rest mass (= m ) and light speed (= c ) from left side of Dirac equation of Eq.5-2 ( this p.23 ),

*(Eq.5-3) Relativistic 1st-order Dirac equation → 2nd-order Klein-Gordon equation*

To obtain the original Einstein relativistic equation and relativistic Klein-Gordon equation with 2nd-order energy (= E^{2} or (cp^{0})^{2} ) from Dirac equation with the 1st-order energy, the relativistic Dirac equation must rely on the nonphysical **4 × 4** γ matrices

↑ Since about this time in 1920s~, quantum field theory has been "**mathematical**" theory rather than "physical" ( this p.7-8 )

Relativistic Dirac equation's nonphysical 4×4 **γ** matrices (= containing four matrices, γ^{0}, γ^{1}, γ^{2}, γ^{3} ) need to satisfy the following condition ( this p.13 ) of

*(Eq.5-4)*

Eq.5-4 means the interchanging different γ matrices becomes the opposite sign (= ex. γ^{2}γ^{3} = - γ^{3}γ^{2} ) called "anticommute" , and the product of the same two γ matrices become γ^{0}γ^{0} = 1 (= or I, which is indentity matrix = " 1 " in the matrix version ) or γ^{j}γ^{j} -1 (= or -I, j = 1,2,3 ).

We often use metric tensor "g" to express the relations of Eq.5-4.

*(Eq.5-4')*

*(metric tensor) -1,+1,+1,+1 version*

4×4 γ marices satisfying Eq.5-4 are

*(Eq.5-5)*

where I means 2 × 2 **identity matrix**.

*(Eq.5-6)*

where σ_{j} mean 2 × 2 Pauli matrices of

*(Eq.5-6')*

↑ This is why physicists started to **baselessly** claim relativistic Dirac equation's nonphysical 4×4 γ matrices including nonphysical 2×2 Pauli matrices (= σ ) might indicate unrealistic "spin" or spinor, though these nonphysical matrices or Dirac equation have **nothing** to do with spin or actual physical phenomena or objects.

For example, γ^{0}γ^{0} = I ( = 4× 4, identity matrix ),

And γ matrices satisfy **anticommutation** relation (= interchanging two different γ matrices gives the opposite sign ) like,

Using above relations of γ matrices, Eq.5-3 is just equal to the following Klein-Gordon equation (= original Einstein relativistic second-order energy-momentum-mass relation ),

*(Eq.4-1) original Einstein relativistic energy (= E ), momentum (= p), mass (= m ) relation*

Other terms such as p^{1}p^{2}, p^{2}p^{3}, p^{1}p^{3}, vanish due to anticommutation relation of γ

Multiplying Dirac equation of Eq.5-1 by cγ^{0} from left side and using **γ ^{0} γ^{0} = 1** and x

Eq.5-7 will be used, when we try to get fictitious Dirac's Hamiltonian (= total ) energy later.

Nonphysical relativistic Dirac fermion's wavefunction ( of nonphysical mathematical particles and antiparticles ) and
**plane wave solution** ( this p.16 ) can be expressed as

*(Eq.5-10)*

In the upper Eq.5-10, ψ^{+} is what they call a "**positive** energy solution" of the alleged Dirac nonphysical particles, and ψ^{-} is a **negative** energy solution of the nonphysical anti-particles ( this p.2-3, this p.4-5 ).

The signs of the energy (= E ) and momentum (= p ) included in the exponential part are the opposite between the particle (= ψ^{+} with e^{ikx} ) and antiparticle (= ψ^{-} with e^{-ikx} ) parts, which is just the **artificially**-created rule **irrelevant** to the real world's phenomena ( this p.6, this p.1,6 ).

And *u(p)* and *v(p)* mean the nonphysical **4 × 1** matrices attached to particle's (= c ) and antiparticle's (= d^{†} ) mathematical operators, respectively ( this p.3 ).

The time (= energy E ) and spatial (= momentum p ) differential acting on exponential functions ( *kx* ) of Eq.5-10 is **equal** to relativistic Klein-Gordon of

*(Eq.4-5)*

and

*(Eq.4-6) E = energy, p = momentum, c is light speed*

Substituting the solutions of Eq.5-10 into Eq.5-1 of Dirac equation, the **positive** energy of a particle is

*(Eq.5-11)*

we use this.

And the **negative** energy part of an antiparticle (= ψ^{-} ) is

*(Eq.5-11')*

These results show that the fictitious relativistic Dirac particle of Eq.5.11 and antiparticle of Eq.5.11' have the **paradoxical** energy-momentum-mass relation (= Not simply positive or negative energies ).

The original Einstein relativistic particle's (= electron ) energy E must be approximately the **sum** of particle's momentum (= p ) and the particle's rest mass energy (= E = cp + mc^{2}, where m and c are the rest mass and the light speed c ).

But the alleged antiparticle's (= positron ) energy E of Eq.5-11' is unrealistic, paradoxical, **inconsistent** with the original relativistic
energy-mass-momentum relation, because this paradoxical antiparticle's energy E is equal to the particle's momentum **minus** the particle's rest mass energy ( E = pc - mc^{2}, this p.7, this p.16, this last, this p.19 ).

↑ The rest mass energy must be always positive with respect to the total energy E (= relativistic Dirac equation represents "free particles", so negative energy or negative rest mass energy are unrealistic ), whether it's a particle or antipaticle, so relativistic Dirac equation contradicts the original Einstein relativity, so wrong.

Dirac equation deals with **free** relativistic particle with **No** potential energy ( this p.3 ), so its relativistic total energy E must be always the sum of the particle's kinetic or momentum energy and (= **plus** ) the particle's rest mass energy (= the absolute value of the total energy E must be always **greater** than the rest mass energy by the positive kinetic or momentum energy ).

But the paradoxical antiparticle's energy E is the kinetic or momentum energy **minus** the rest mass energy. ← The absolute value of the total energy E of the free antiparticle (or positron ) becomes paradoxically **less** than the rest mass energy, which **contradicts** the original relativity.

↑ This unrealistic energy of the antiparticle has **nothing** to do with the issue of negative energy. The real problem is the **signs** of the energy-momentum (= E,p ) and the rest mass energy (= mc^{2} ) are always **opposite** only in the fictitious antiparticles.

From Eq.5-11 and Eq.5-11', matrices of u(p) and v(p) need to satisfy the following relation in (-1,+1,+1,+1) version of Dirac equation,

*(Eq.5-12)*

*(Eq.5-13) antiparticle part satisfies*

Here we used Eq.5-14 and Eq.5-15

*(Eq.5-14)*

In Eq.5-14, u^{†}(p) (**1 × 4** matrix) means the " complex conjugate transpose" (= change the sign of the imaginary number i → -i, and change it into the transposed matrix, this middle ) of u(p).
u^{†}(p) = (u(p)^{*})^{T} this p.8

The bar-u or bar-v of the upper Eq.5-12-Eq.5-14 means the complex conjugate transpose u^{†} multiplied by γ^{0} matrix from the right side ( this p.12 ).

The artificial notation of bar-ψ or bar-u in the above Dirac equation means the complex conjugate transpose (= ψ^{†} or u^{†}, this p.8 ) times unphysical γ^{0} matrix, which are just the artificially-created concepts **irrelevant** to the real world's phenomena.

Basically, the form of this unphysical relativistic Dirac equation does not change in its conjugate transpose (= bar-u and bar-v ) or adjoint version ( this p.8, this p.6, this p.89 (or p.60 ), this p.19-(10.148) and p.23-(10.166) ). ← If you want to change the notation from the this website's (-1,1,1,1) to (1,-1,-1,-1) version, change the sign like γ^{μ}p_{μ} → -γ^{μ}p_{μ} as shown in this.

↑ This **artificial** ad-hoc notation of adjoint × γ^{0} matrix is necessary in (pseudo-)relativistic Dirac equation, because the nonphysical 4×4 γ^{j} matrices (= j = 1,2,3 components ) are anti-Hermitian or Not Hermitian (= complex conjugate transpose of γ^{j} matrices γ^{j †} are Not equal to the original γ^{j} matrices, this p.2-lower-p.3-upper, this p.3-(75) ), which is undesirable in the mathematical world of quantum field theory.

So the γ matrices allegedly representing 4×4 matrix-spin are completely different from 2×2 Pauli matrices (= the complex conjugate transpose of Pauli matrices are equal to the original Pauli matrices like σ^{†} = σ = Hermitian, this-(2.4.12) ) in their mathematical properties.

In spite of this discrepancy, the relativistic quantum field theory baselessly claims that Dirac equation have the property of (unphysical) spin, just because its nonphysical γ matrices contain Pauli σ spin matrices without showing any more detailed physical mechanism of "spin".

We multiplied the first equation of Eq.5-14 by γ^{0} from right side, and use the relations of

*(Eq.5-15) γ ^{†} = complex transpose of γ*

The relation of Eq.5-15 can be proved using Eq.5-5, Eq.5-6 and Pauli matrices σ^{†} = σ of Eq.5-6'.

( anticommutation of γ^{0}γ^{i} = - γ^{i}γ^{0}, and γ^{0}γ^{0} = 1. )

In all cases of μ= 0, 1, 2, 3, Eq.5-15 holds true.

*(Eq.5-16) artificial definition of bar-u*

As shown in the upper Eq.5.16, the bar-u means the complex conjugate transpose or adjoint (= u^{†} ) of u matrix × γ^{0} matrix.

Using Eq.5.14 and Eq.5.16, we can get the right equation of Eq.5-12.

To satisfy Eq.5-12 equation, we can **artificially** adjust the coefficient **parameter** of the particle solution's unphysical Dirac matrix = u(p) = 4×1 matrix as ( this p.3-4 )

*(Eq.5-17) Unphysical Dirac matrix inside Dirac wavefunction*

( This Dirac particle's solution u(p) **must** include nonphysical matrices γ^{μ}. )

↑ As shown in this, we can **freely change** and redefine each coefficient **parameter** inside the Dirac wavefunction, so any calculations based on these freely-adjustable parameters of Dirac wavefunction, quantum field theory and QED are **meaningless** with No power to predict any physical values.

Substituting Eq.5-17 into the left equation of Eq.5-12,

*(Eq.5-18) Dirac equation (parameter) is secretly adjusted to satisfy the failed Klein-Gordon (= Einstein relativistic ) equation.*

Eq.5-18 means that Dirac spinor of Eq.5-17 satisfies the failed *Klein-Gordon* equation ( this p.20-21, this p.33-34 ).

↑ So "Dirac equation obtained "spin = nonphysical γ matrices" due to its **square root** of relativistic second-order Klein-Gordon equation" is a **lie**, because physicists **secretly** inserted one of "square-roots" into the freely-manipulable coefficient parameters of the particle's (or antiparticle's ) Dirac solutions !

So the **failure** of the 1st relativistic Klein-Gordon equation means the **failure** of the similar Dirac equation.

In the same way (= for nonphysical Dirac antiparticle to **secretly** satisfy Klein-Gordon equation, while the fatal paradoxical energy-mass relation still remains ), the solution v(p) can be defined as

*(Eq.5-19)*

Substituting the upper Eq.5-19 into Eq.5-13, the solution Eq.5-19 proves to satisfy Klein-Gordon equation.

The problem is Dirac equation for getting relativistic spin-orbit fine structure of hydrogen atom does Not use these Dirac free particle's solution (= u, v = artificially satisfying relativistic Klein-Gordon equation ), instead, Dirac hydrogen uses **irrelevant** nonrelativistic Schrodinger's hydrogen's spherical Harmonics, hence, Dirac hydrogen is **inconsistent** with relativistic Einstein energy relation (= or Klein-Gordon equation ), and wrong.

Replacing γ^{μ} matrices of Eq.5-17 by Eq.5-5 and Eq.5-6, the *numerator* of Eq.5-17 can be expressed as

*(Eq.5-20)*

where we use Eq.1-6. And p_{j}σ_{j} means the sum of 1-3 components (= x,y,z components ) of p_{j}σ_{j} where p is the particle's momentum and σ is Pauli 2×2 matrix.

They **artificially** defined the matrices of **u(0)** and **v(0)** in Eq.5-17 and Eq.5-19 as ( this p.3, this p.10-12 )

(*Eq.5-21*) *Unphysical Dirac 4×1 spinors*

So u(0) is the *upper* two componetns, and v(0) is the *lower* two components.

↑ These artificially-defined nonphysical Dirac matrices have **nothing** to do with real physical phenomena or imaginary "spins ( this p.16-17, this p.4 )".

As shown in this p.34, using Eq.5-20, Eq.5-17 is equal to the following (= its coefficient can be freely adjusted to different values, this p.3 )

*(Eq.5-22)*

*(Eq.5-23)*

So the complex conjugate transpose of u(p) × γ^{0} (= Eq.5-16) = bar-u 1×4 matrix can be expressed as

*(Eq.5-24)*

where Pauli matrices σ^{†} = σ.

Using Eq.5-22 and Eq.5-24,

*(Eq.5-25)*

*(Eq.5-26)*

here we use Klein-Gordon equation and *σ _{j} σ_{j} = 1* and anticommutation in Pauli matrices. (See Eq.5-6' ).

Substituting Eq.5-26 into Eq.5-25, we can get ( this p.4, this p.3 )

*(Eq.5-27)*

*(Eq.5-28)*

where the subindex σ of φ_{σ} means **nonphysical** "spin ( σ = ↑ or ↓ )" of Eq.5-23.

And when we calculate in the same way as that of u(p), we can get

*(Eq.5-29)*

↑ All these calculation values are physically **meaningless** and useless, because all these coefficient parameters of the alleged nonphysical Dirac's particles (= u ) and antiparticles (= v ) can be **freely changeable** to obtain the desirable results.

And if we **delete** γ^{0} in Eq.5-24, we have ( this p.2-lower )

*(Eq.5-30)*

In the same way,

*(Eq.5-31)*

So Eq.5-30 is equal to Eq.5-31 in the case that γ^{0} is deleted.

Artificially-created relativistic Dirac Lagrangian leading to Dirac's equation can be defined as

*(Eq.5-32) artificial Dirac Lagrangian (= L )*

This Lagrangian is said to be Lorentz invariant scalar.

As I said, Lagrangian (= L ) itself has **No** physical meaning except for a "tool" to get some particle's equation of motion and Hamiltonian (= total ) energy through some artificial procedure called Euler-Lagrange equation, and these relativistic Dirac and Klein-Gordon equations' Lagrangians were **artificially**-created, and **inconsistent** with the original Lagrangian form (= L = kinetic minus potential energy ).

First, with respect to conjugate transpose of ψ (× γ^{0}), Euler-Lagrange equation (= to obtain Dirac equation ) is

*(Eq.5-33)*

where the second term of Eq.5-33 is *zero*. (= because Dirac Lagrangian of Eq.5-32 doesn't include the derivative of the bar-ψ )

So the first term of Eq.5-33 is ( using Lagrangian L of Eq.5-32 )

*(Eq.5-34)*

Eq.5-34 is equal to Dirac equation of Eq.5-1.

So by applying Euler-Lagrange equation to the artificially-created Dirac Lagrangian (= L ) with respect to the adjoint-ψ, Dirac equation can be obtained.

And the **nonphysical** conjugate transpose (= adjoint ) of Dirac equation (Eq.5-1) is

*(Eq.5-35) Dirac equation's adjoint 2nd-version.*

where we use Eq.5-15 and multiply it by γ^{0} from the right side.

The direction of the differentiation is *opposite* from Eq.5-1, but the meaning of Eq.5-35 is supposed to be equal to Eq.5-1 (= these mathematically-defined equations do **Not** represent real phenomena, anyway ).

When using the usual ψ(x) in Dirac Lagrangian and Euler-Lagrange equation, we can obtain the adjoint form of Dirac equation ( this p.8, this p.7, this p.7 )

*(Eq.5-36)*

Eq.5-36 is equal to Eq.5-35.

As a result, we can get Dirac equation from the artificially-created Dirac Lagrangian of Eq.5-32.

↑ In other words. in order to get Dirac equation (= there are two versions of original Dirac equation and its adjoint ), its **unphysical** Lagrangian (= L ) was **artificially** created and chosen.

So these procedures to get Dirac equation from the artificial Lagrangian have **No** physical meaning.

Artificially-created Dirac Lagrangian (= L ) is also used to obtain Dirac version of Hamiltonian energy (= relativistic Dirac free particle's total energy ) and the fictitious momentum (= p or π ) by copying the classical mechanical Hamiltonian procedure called Legendre transformation ( this p.9-10, this p.4-5 ).

The problem is this momentum obtained by this Hamiltonian procedure is **Not** a real momentum in Dirac and Klein-Gordon equation, unlike the ordinary classical mechanics.

Relativistic quantum field theory and QED like to use
the fictional concepts called the generalized (= canonical ) momentum (= π or p, ) based on wrong math, which is **Not** a real momentum expressed as mv (= mass × velocity, this middle ).

This **fictional** canonical **momentum** (= p or π ) obtained from the artificially-created Dirac's Lagrangian and this (classical) transformation becomes ( this p.16 )

*(Eq.5-37) Dirac's fictional (canonical) momentum = π*

↑ This artificially-created canonical momentum (= π = iℏψ^{†} = complex conjugate ) including No mass or velocity is completely **different** from the true momentum expressed as the particle's mass × velocity. ← Relativistic quantum field theory **lacks** reality in their unphysical momentum from the beginning.

From this fictional momentum (= π ) and Lagrangian (= L ), using this procedure, the relativistic Dirac's fictitious Hamiltonian total energy (= H ) is supposed to be ( this p.3-5, this p.2-4 )

*(Eq.5-38) Fictitious Dirac Hamiltonian (= total ) energy (= H )*

where the last equation of γ^{j}∂_{j} means the sum of 1-3 components (= x,y,z components ) with respect to "j" like γ^{1}∂_{1} + γ^{2}∂_{2} + γ^{3}∂_{3}.

From Eq.5-7, Eq.5-38 is equal to ( this p.2, this p.17 )

*(Eq.5-39) Dirac unphysical Hamiltonian energy*

And the Dirac wavefunction solution containing nonphysical math particles ( this p.5-6, this p.98-100 ) used in Hamiltonian of Eq.5-39 is expressed as

*(Eq.5-40) ↓ Nonphysical Dirac wavefunction, c or d is a particle or antiparticle.*

As shown in the above Eq.5-40, the most widely-used important relativistic Dirac equation's solution just expresses each fermion such as an electron, a quark or an antiparticle just as **nonphysical** math symbols with No realistic figures ( this p.19, ).

The coefficient of the upper Eq.5-40 Dirac solution can be **freely changed** together with other artificially-manipulable coefficients of unphysical spinor relations of u and v, and the coefficient of the particle's anticommutation relation (= as I explain later, this anticommutation represents unphysical Pauli principle ) to obtain the desirable Hamiltonian energy's form ( this-(5.4),(5-5),p.3-last, this p.151-(X.4)-(X.5)-p.153 ).

↑ These artificially-changeable coefficients of Dirac equation is Not a prediction of the theory, but just a artificial manipulation or choice of coefficient parameters ( this p.22 ), so relativistic Dirac equation has No power to predict anything.

The exponential function in the upper Dirac wavefunction contains particle's energy and momentum

And Dirac wavefunction's conjugate transpose or adjoint form (× γ^{0}) is

*(Eq.5-41) Relativistic Dirac plane wave solution, bar-ψ = adjoint × γ ^{0}*

The bar-ψ of the upper Eq.5-41 is the conjugate transpose or adjoint form × γ^{0} matrix of the relativistic Dirac wavefunction or spinors ( this p.8 ).

These u(p) and v(p) are 4 × 1 spinors in Eq.5-17 and Eq.5-19, respectively.

And *c(k) (+ u )* and *d(k) (+ v )* mean **annihilation** operators of particle and antiparticle, respectively.

So c^{†}(k) and d^{†} (k) are nonphysical **creation** operators with No particle's figures, which abstract math symbols tell us **nothing** about the detailed physical mechanism of relativistic quantum field theory.

Substituting Eq.5-40 into Eq.5-39, and using Eq.4-5, Eq.5-30 and Eq.5-31, we can get the nonphysical Dirac Hamiltonian (= H, this p.5, this p.3-5, this p.26-28 )

*(Eq.5-42) Fictional Dirac Hamiltonian energy, c ^{†}
= particle, d^{†} = antiparticle*

c^{†} (= particle creation operator ), d^{†} (= antiparticle creation operator )

c (= particle's annihilation operator ), d (= antiparticle's annihilation operator ).

n = c^{†}c (= or a^{†}a ) in Hamiltonian energy (= H ) is the particle's number operator (= which is just an artificially-introduced rule, hence, has **No** physical meaning, this p.4 ).

Using the artificially-prepared Dirac wavefunction, only the antiparticle's part becomes the opposite of number operator (= dd^{†} ) attached to the negative energy (= -E = -ℏω )

For example, in the actual calculation to get this Dirac Hamiltonian energy, using Eq.5-40, the c^{†}c part (= particle energy part ) of Eq.5-39 is

*(Eq.5-42')*

↑ All these calculations of Dirac particle's energy are physically **meaningless**, because they can freely manipulate the coefficient parameters (= so the resultant Hamiltonian energy can be also freely manipulated ) of Dirac wavefunction

Due to the minus sign of antiparticle part = the first equation in Eq.5-42' (= red line ), the antiparticle's Hamiltonian energy = d d^{†} part of Eq.5-42 becomes **minus** (= negative energy problem ? ), when the time (= energy ) derivative (= iℏ∂_{t} ) acts on e^{-ikx} = e^{iωt}

↑ This antiparticle's negative energy was artificially-prepared (= Dirac wavefunction ψ itself was artificially introduced ), so this mathematical antiparticle has **No** physical meaning.

δ(k-k') is unphysical Dirac delta function.

*(Eq.5-42'') ↓ Only antiparticle (= d ^{†} ) energy has the minus sign (= negative energy ? ), which must be fixed using unphysical Pauli exclusion principle ?*

To get the **positive** number operator like n = **d ^{†}(k) d(k)** from the antiparticle Hamiltonian energy part of Eq.5-42, physicists insist the following artificial

*(Eq.5-43) ↓ This relativistic quantum field theory just showing the meaningless abstract math relation of "anticommutation" tells us nothing about the detailed mechanism of Pauli principle !*

Relativistic quantum field theory claims this **abstract meaningless** math relation called "anticommutation ( this p.3 )" is the **only** explanation for mysterious **Pauli exclusion principle**, without showing any more detailed mechanism ( this p.5, this p.5, this p.4, this p.2 ). ← Our science stops progressing by **stopping** delving into deeper detailed mechanism of how exactly this Pauli principle repulsive force is generated.

The notation about the above anti-commutation relation of (unphysical) particles is like in this p.3-(16), this-(8.2.11-14).

δ(k-k') is unphysical Dirac delta function, which is used just as one of **artificial rules** (= the upper coefficient of δ function can be freely changed ) that has **Nothing** to do with any real physical principle.

Using this artificially-introduced unphysical anticommutation rule of Eq.5-43, the Dirac Hamiltonian's antiparticle negative energy part of Eq.5-42 becomes the following Eq.5-44

*(Eq.5-44) ↓ Only this meaningless math proves Pauli principle mechanism ? ← impossible ! No real physical picture or mechanism is shown !*

In the last line of the upper Eq.5-44, we can get *positive* number operator of d^{†}(k) d(k) (= *positive energy* in both particles and antiparticles ) using the artificial rule of anticommutation allegedly indicating Pauli exclusion principle.

So they insist Eq.5-43 represents the mysterious force of **Pauli exclusion principle** ( this p.4.5,7, this p.5-6, this p.16-17, this p.4-lower ).

↑ But they just show very abstract meaningless math relation called anticommutation (= exchanging two nonphysical math operators gives the opposite sign = proof of Pauli principle ? ← No way ! ).

Furthermore, in this process, physicists are saying the **contradictory** thing about this nonphysical anticommutation Pauli principle.

Because to eliminate the negative energy of antiparticle, they artificially created new negative vacuum energy (= minus δ(0) delta function in the last line of the upper Eq.5-44, this p.5-(5.17), this p.4-lower, this p.23-(4.35) ), which means the unrealistic negative infinite energy **remains**, whether the meaningless Pauli principle's anticommutation rule is introduced or not.

This annoying negative **infinite** vacuum energy (= -δ ) may be canced out by the positive infinite vacuum energy of the failed Klein-Gordon's equation using the imaginary nonphysical theory called "supersymmetry ( this p.23-second-paragraph, this p.13 )".

↑ But we can**not** use the failed Klein-Gordon equation to artificially cancel this Dirac's infinite negative energy (= first, Dirac's equation represents "free relativistic particle with **postive** rest mass + kinetic energies and No potential energies" which can**not** generate the negative infinite energy ! So this unphysical negative vaccum energy is unjustifiable ).

And even if they manage to artificially cancel this infinite vacuum energy (= called infrared divergence ), they have to deal with other more **serious infinity** caused by infinite virtual particles (= called ultraviolet divergence, this p.5 ).

This result shows that the commonly-used phrase "Dirac antiparticle could solve negative energy !" is a total **lie** (= They just artificially introduced these meaningless math equations with **No** relation to the real world ), and the antiparticle's **paradoxical** energy-mass relation remains unsolved.

And if Eq.5-43 needs to be satisfied, the relation of ψ and its **fictional momentum** π or iℏψ^{†} (= Eq.5-37) becomes

*(Eq.5-45) π = ψ ^{†} = Dirac fictional momentum*

This anticommutation relation of Dirac's **fictional** canonical momentum ( this p.1,6, this p.2,5 ) is different from Eq.4-24 of Klein-Gordon equation, which means Dirac's fictional momentum of Eq.5-45 is **inconsistent** with the original quantum mechanical commutation between position (= q or x ) and momentum (= p or spacial derivative ) operators based on de Broglie's relation of

*(Eq.4-25)*

If we define the new property of canonical momentum like Eq.5-45 (= anticommutation ), we have to find out the **new theory** which replaces de Broglie's theory.

But the experimentally-verified de Broglie's theory is a basic one in the quantum mechanics, which can not be eliminated.

Can we use π of Eq.5-37 as a *canonical momentum for getting Hamiltonian*, though it does NOT obey de Broglie relation ?

It is **unacceptable**.

*(Eq.5-46) ↓ This nonphysical abstract equation represents (fictitious) photon (= A ) and electron (= ψ) interaction ? ← No more detailed mechanism, so useless.*

Physicists try to combine the fictional Lagrangians of electromagnetic theories and artificial Dirac electron's Lagrangian to produce the **virtual** interaction between electrons and unreal virtual photons for QED infinity calculation ( this p.9, this p.10-13, this p.1-5 ).

↑ Both these Dirac electron (= ψ ) and (virtual) photons (= A ) are expressed just as **nonphysical** abstract math symbols which tell us **nothing** about the detailed interaction between electrons and (virtual) photons.

*(Eq.5-46') ↓ Wrong replacement for fictional interaction between Dirac electron and unreal virtual photons causing meaningless QED infinity.*

Interaction term ( of particle and vector potential A allegedly containing unreal virtual photons ) of Eq.5-46 is

*(Eq.5-47) Fictional interaction term between electrons (= ψ ) and virtual photon (=A ).*

Relativistic quantum electrodynamics (= QED ) calculation using this **fictitious** interaction between photon (= electric and magnetic potential A ) and electron (= Dirac wavefunction ψ ) is mathematically wrong, because QED tries to obtain very tiny finite physical values (= anomalous magnetic moment or g-factor ) by the **illegitimate** renormalization method of artificially subtracting **infinity** from another freely-adjustable **infinite** bare parameters (= Indefinite "infinity" itself cannot be defined or used as the "predicted value", at all, this p.8-9, this p.11-13 ).

↑ Infinity minus infinity = **uncertain** and indefinite finite value, because "infinity" itself is an **indefinite** uncertain value. So QED renormalization method based on this uncertain and unpredictable value is an illegitimate and **wrong** math.

The problem is the original Lagrangian between charged particles and the electromagnetic photon (= A ) was created based on **nonrelativistic** energies (= E = p^{2}/2m, Not based on relativistic E^{2} = p^{2} + mc^{2} ), so this interaction term cannot be used in relativistic Dirac electron or QED due to the **lack** of theoretical basis. ← QED is false.

Furthermore, the theory for getting this fictitious photon-electron interaction inside electromagnetic Lagrangian or Hamiltonian energy (= H ) uses wrong math, so all the relativistic quantum field theory such as QED and standard model based on this wrong interaction term between Dirac electron and virtual photon is illegitimate and **invalid**.

**Comparing** Eq.5-46 (= mixed Lagrangian consisting of photon and Dirac equation ) with Eq.3-2 (= electromagnetic Lagrangian ) and Eq.3-3 of

*(Eq.3-2) Fictitious electromagnetic Lagrangian where A is electronc and magnetic potential containing fictitious photon, J is electric current. *

and

*(Eq.3-3) Euler-Lagrange equation for obtaining Maxwell equation*

They **rashly** started to claim that (fictitious) Dirac's electric current (J) density (= correspond to the classical electric current, they thought ) becomes

*(Eq.5-48) ↓ Electric current (= J ) represented by unreal Dirac electron wavefunction (= ψ ) and unphysical γ ^{μ} matrices*

Using the fictional current j in the upper Eq.5-48, physicists baselessly claim that Dirac equation has succeeded in expressing the (fictional) electric current density (= j ) ( this p.2-lower, this 10th-paragraph ).

But as shown in Eq.5-6, γ matrices *consisting of mathematical Pauli spin matrices* have **nothing** to do with the direction of the electric current, contrary to Dirac fictional current J using this γ matrices as the current's direction (= J_{μ} = γ_{μ}, where the component μ means the fictional direction of the current J ) as shown in the upper Eq.5-48.

4×4 γ matrices are supposed to represent (nonphysical) **spin** components of Dirac equation, which have **NO relation** with the direction of current.

But in Eq.5-48, this spin component (= μ of γ_{μ} ) decides the direction of the current J_{μ}.

So Eq.5-48 and Eq.5-47 are based on *wrong interpretation*.

By the way, why have we gotten the wrong result of Eq.5-48 in Dirac equation ?

In fact, γ matrices (= σ matrices) are not peculiar to Dirac equation.

Even in Schrodinger equation (or classical mechanics with No spin ), **σ matrices are included**, as follows,

*(Eq.5-49)*

Here we use the following relations of Pauli (= σ ) matrices.

*(Eq.5-50)*

When a particle is under Lorentz force of Eq.2-13 (= causing fictitious photon-electron interaction based on wrong math ), the quantum mechanics uses the mathematical tricks like

*(Eq.5-51)*

where p includes derivative (= based on de Broglie relation ), which acts on before and after A_{j}.

So de Broglie wavelength of the particle is also used in derivative (= ∂ = ∇ ) of the vector potential (= A ) to get the magnetic field (= B = ∇×A = ∂_{i}A_{j} - ∂_{j}A_{i}, ← this derivative ∂ originated from the irrelevant electron's de Broglie wave ).

This is strange, becuase they insist *electron's de Broglie wave = external magnetic field*.

and we also use the trick of

*(Eq.5-52)*

Considering Eq.5-50, Eq.5-51 and Eq.5-52, Eq.5-49 under the replacement of Eq.2-13 changes to

*(Eq.5-53)*

Eq.5-53 and Eq.5-52 mean that *spin-magnetic field* (= vector potential) interaction (= SB = 1/2σB where σ is Pauli spin matric ) exists in **Schrodinger equation**, too.

And to agree with **Bohr magneton** ( of Bohr model ), spin g factor g_{e} must be "2".

↑ The fact that the nonrelativistic Schrodinger equation **without** spin also tacitly **includes** the Pauli σ spin matrices means relativistic Dirac equation's unphysical γ matrices consisting of Pauli σ matrices have **nothing** to do with (fictitious) spin.

Partial differentiation of Lagrangian ( L_{I} = - H_{I} ) of Eq.5-53 by the vector potential (A) is

*(Eq.5-54)*

The electric current (J) in Schrodinger equation consists of charge and its **velocity**, as shown in Eq.5-54.

( Here Eq.2-13 is used. )

And σ matrices is **hidden** as σσ = 1 as shown in Eq.5-53, which is NOT used in Schrodinger equation current.

On the other hand, the (fake) relativistic Dirac equation is **first** order in the momentum as shown in Eq.5-46, unlike the original nonrelativistic Schrödinger equation's second-order momentum.

(So also in the vector potential A, it is first order in Dirac equation, which is different from classical electromagnetism. )

As a result, differentiation with respect to vector potential (A) **erases the particle's momentum** expressed as the derivative (= ∂ ) in Dirac equation !

(So there is *NO charge's current* at this point in Dirac equation. )

This means that the **first order** Dirac equation, which is unable to give real electric current, can **NOT** use the replacement of Lorentz force (= Eq.2-14 ) correctly !

(Interaction of Lorentz force is "**originally**" considered in the **second order** equations of classical mechanics. )

But this (fictitious) replacement of Lorentz force is used as the (fictitious) interaction term between virtual photon and electron of Eq.5-47 in the quantum electrodynamics and standard model, which means All these QED and standard model using wrong photon-electron interaction term are wrong, too.

*(Fig.P) ↓ A relativistic photon is just a unphysical math symbol where "zero component photon" generates the contradictory negative probability. ← QED is false.*

In fact, all the relativistic quantum field theory, quantum electrodynamics (= QED ) and standard model are **unable** to describe the light wave's imaginary particle called "photon" in the realistic way.

All the current relativistic quantum field theoy can do is show very **abstract** math symbol or creation ( annihilation ) operator as an invisible imaginary photon particle (= each fictitious photon is expressed just as the abstract symbol a^{†} ? ), which can tell us nothing about the detailed behavior and shape of a photon ( this p.338 ).

Relativistic quantum field theory and QED claim that an infinite number of fictitious (mathematical) photon particles constitute the magnetic vector potential (= A_{j}, j = 1,2,3, this p.2-left, this p.3 ) and electric scalar potential (= φ ) with No more detailed description about the mysterious photon's figure. = Science **stops** delving into deeper truth.

In the current electromagnetic theory, the **fictitious** unobservable concept called "gauge" is introduced as a freely-changeable parameter, which allegedly doesn't affect the observable electric and magnetic field. ← But this is **untrue**, the relativistic quantum field theory and QED destroy and drastically change the original Maxwell equation due to this meaningless restriction on the unphysical gauge ( compare this p.6 and p.14 ).

Physicists try to restrict this free fictitious parameter "gauge" to impose various additional rule on the original Maxwell equation.

One simplest artificial condition is called "Coulomb gauge" where the realistic electric potential (= φ caused by the charged particle ) is forced to be **zero** and unavailable (= electric scalar potential φ = 0 ).

This artificial restraint removing the zero component (= A^{0} = φ/c = 0, where φ is electric scalar potential, this p.7, this p.2 ) of electromagnetic field makes this Coulomb gauge **violate** Einstein relativity ( this p.4-lower, this p.5-3rd-paragraph, = artificial Coulomb gauge condition breaks relativistic Lorentz invariance ), hence, this contradictory Coulomb gauge is Not used in the authentic relativistic quantum field theory or QED.

In this simplest Coulomb gauge, each **unphysical** photon expressed as an abstract math operator (= a_{j} ) is supposed to have two types of transverse polarizations ( this p.6-8, this p.6-7 ) with No more detailed description than this abstract meaningless math symbols. ← How and what shape of polarization each (fictitious) photon has is **unknown** in this very abstract unphysical math symbol photon of quantum field theory.

Another widely-used gauge restraint condition is called "Lorentz gauge ( this p.4-6 )", which is equal to "Feynman gauge ( this p.8-(6.37), this covariant approach )" which is said to obey Einstein relativity, due to its Lorentz invariant property (= any observers can see the same physical principle, this, this p.8-upper, this p.5, this p.8 ).

Electromagnetic wave or photon is known to have two types of transverse polarizations (= 1,2 components ) where the longitudinally-polarized light wave or photon should Not exist.

But the relativistic quantum field theory or QED allegedly compatible with Einstein relativity must include these two more excessive unrealistic photon's polarizations, the longitudinally-polarized photon (= 3 component ) and the scalar (= time-like) zero-polarized photon (= 0 component, this p.3 ) expressed as nonphysical math symbols with No concrete figure ( this p.5-left-lower, this p.8-(51), this p.2,7 ).

This so-called **relativistic** electromagnetic theory using Lorentz (= or Feynman ) gauge must include the **unrealistic** scalar (= time-like ) zero-polarization photon (= which means the unreal zero component photon with No polarization, this p.47-50 ) constituting the electric potential (= φ ) = they baselessly argue Coulomb electric force is caused by this unreal **scalar virtual** photon.

To satisfy Einstein relativistic Lorentz invariance (or symmetry ), this unreal scalar photon must have the unphysical **negative probability** (= this p.2-right-upper, this p.5-6, this p.10-(6.50) ) ! This unreal scalar-polarized (= time-like ) photon with negative probability or negative norm is physically impossible ( this p.3-4, this-6.542, this 2nd-paragraph, this p.15, this p.3 ).

Relativistic quantum field theory and QED needs (unreal) virtual photons to explain the electric and magnetic forces, and they baselessly insist this unobservable unreal virtual photons can have (unreal) longitudinal polarization ( this p.28-last, this p.25(or p.23 )-last-paragraph, this p.8 ) and the scalar-time-like-polarization ( this p.9-upper, this p.16-2nd-paragraph, this p.8. this p.7-1st-paragraph ).

So all the relativistic electromagnetic quantum field theory and QED are **wrong** due to this unrealistic longitudinally-polarized photon and the zero-polarization scalar (= time-like ) photon with negative probability that is necessary to explain some phenomena such as Coulomb elecric interaction based on (unreal) quantum virtual photons ( this p.4 3rd-paragraph, this p.4-right-5th-paragraph, this p.8-last-sentence, this p.3-first-paragraph ).

↑ Physicists try to artificially redefine the "vacuum" to eliminate this unreal scalar photon from the relativistic QED ( this p.18-19 (or p.22-23) ), but this unreal scalar photon or Feynman (= Lorentz ) gauge is used and necessary for any relativistic QED calculations (= relativistic theory always needs four-components of all concepts also in imaginary polarizations ) as a propagator of (unreal virtual) photons ( this p.12, this p.9, this p.9, this p.14(or p.26), this p.9, this p.12-right ).

If (unreal) longitudinal-polarized and negative-probability-scalar (= time-like ) photons are unnecessary, physicists should have created a new theory without them, but they couldn't.

Quantum mechanics and relativistic QED definitely need unphysical (virtual) photons with unreal longitudinal and zero-polarized photons to satisfy Einstein relativistic theory or Lorentz (= Feynman ) gauge that always needs four-kinds of photon polarizations like four-spacetime-vectors ( this p.97-98, this p.8, this p.4 ).

Contrary to the media and academic **hypes**, the relativistic quantum field theory and QED have **No** power to describe and clarify the exact detailed physical mechanism of how each electron interacts with a (imaginary ) photon, and QED has No power to predict physical values (= this is why the media just repeats the empty cliche "successful QED !", and **never** presents us with their **dubious** detailed calculation methods, this p.3-left ).

QED just shows the abstract simple Feynman diagram ( this p.58, this p.9 ) where each electron expressed as the abstract math symbol ( this p.11-13 ) is said to interact with infinite unreal virtual photon violating Einstein relativity ( this p.13 ) with infinite amount of energies ( this p.29-last-paragraph ).

All calculation values of this unrealistic QED miserably **diverge to infinity** ( this 21 5th-paragraph ) due to the infinite **unreal** virtual photons, which mathematically-meaningless infinity must be artificially removed by another unobservable **infinite free parameters** or counterterms called "bare charge and mass" which ad-hoc method is called renormalization ( this p.28, this p.40-41, this p.67-68(or p.60-61) ). This illegitimate ad-hoc QED is useless with No power to predict any values (= anomalous magnetic momenet or g-factor was obtained just by freely adjusting these uncertain infinities, which is Not math or predicting values, this 1st-paragraph ) .

*(Eq.6-1) Electric (= E ) and magnetic (= B ) fields are unchanged under the artificial gauge transformaiton (= f ) in the magnetic vector (= Ai ) and electric scalar (= φ ) potential ?*

The present quantum field theory focuses only on the unobservable = physically **meaningless** concepts such as fantasy quantum parallel-worlds and extradimensions, so useless.

Relativistic quantum field theory and QED also consider the physically-meaningless fictitious concept called "gauge (= f )" as a important tool to manipulate QED parameters.

Under this artificial gauge transformation in the upper Eq.6-1, the observable electric (= E ) and magnetic (= B ) fields are said to be unchanged. ← But this is a total **lie**, as I explain later.

Relativistic quantum field theory uses the unobservable fictitious concpets such as the magnetic vector (= three components of A1, A2, A3 = Ax, Ay, Az ) and electric scalar (= φ = zero componenet of A0 ) potentials to describe the observable electric and magnetic fields.

↑ So physicists claim this degree of freedom in choosing the fictitious gauge allows them to artificially choose various gauge conditions such as Coulomb gauge and Lorentz gauge in the quantum field theory, which is a meaningless theory.

But in fact, all these gauge conditions such as Coulomb gauge and Lorentz gauge used in relativistic QED **break** and drastically change the meaning of the original Maxwell equation, so
all the relativistic quantum field theoies, QED and standard model relying on this fictitous gauge theory are **inconsistent** with the experimentally-verified Maxwell theory. ← QED is **false**.

In the relativistic QED, physicists often choose the fictitious gauge f(x) which satisfies the relativistic Lorentz invariance (= form of equation is unchanged under Lorentz transformation ). which is called Lorentz gauge or Feynman gauge ( this p.4 ) like,

*(Eq.6-2) Lorentz (or Feynman ) gauge condition*

We use (-1,+1,+1+1 ) version of metric tensor.

So only the sign of the zero component vector is changed depending on the index position ( A^{0} = -A_{0} = φ/c, A^{j} = A_{j} when j = 1.2,3 )

The reason why physicists tend to choose this Lorentz gauge condition is to keep the Maxwell's equations *Lorentz-invariant*.

Eq.6-2 is scalar form (= unchanged under Lorentz transformation due to the form of a pair of covariant and contravariant vectors, this p.8-upper ).

Under Lorentz transformation, the form of Lorentz gauge condition of Eq.6-2 is **unchanged** like

*(Eq.6-3)*

So we can prove Eq.6-2 (= Lorentz gauge condition ) is Lorentz invariant ( this p.7-8 ).

Using Eq.3-1 ( this p.2 ), Maxwell equations of Eq.3-3 can be expressed using magnetic (= Ai ) and electric potentials (= A0 ) as

*(Eq.6-4) Original (unbroken) Maxwell equation ↓*

↑ This form of Eq.6-4 is the original authentic Maxwell equation using magnetic and electric vector potentials (= A ) and the electric current (= J ).

But using the Coulomb gauge or the relativistic QED Lorentz gauge condition of Eq.6-2 ( this p.6,14 ), Maxwell equations of Eq.6-4 is **destroyed** and completely changed into

*(Eq.6-5) Lorentz gauge and Coulomb gauge destroy the original Maxwell equation, so wrong.*

where the magnetic potential A_{1} is supposed to be constant (= time derivative of A_{1} or ∂_{0}A_{1} =
∂A_{1}/c∂t is zero, which means electric current J_{1} is constant ), while the electric current of J_{2} or J_{3} is not constant (= space derivative of A_{2} or A_{3} is not zero ).

↑ This destroyed Maxwell equations by imposing fictitious Coulomb gauge ( this p.16(or p.12)-(1.6), this p.5-(6.19) ) or relativistic Lorentz gauge rules ( this p.3-lower, this p.11-(86), this p.4-(16.16), this p.4-lower ) are clearly **different** from the original Maxwell equations.

This means the restriction by Lorentz gauge or Coulomb gauge, which completely destroys and alters the original authentic Maxwell equation, is **invalid**, and unreal longitudinal and scalar-polarized photon with negative-propability cannot be eliminated by gauge restriction in the relativistic quantum field theory and QED.

↑ Only one-component magnetic vector potential A_{μ} or A_{j} ( in Coulomb or Lorentz gauge electromagnetic equation ) is Not enough to make the magnetic field B, which requires at least two different components like B_1 = ∂_{2}A_{3} - ∂_{3}A_{2} = two components A_{2} (= Ay ) and A_{3} (= Az ) are necessary for describing the magnetic field B.

Here we consider the **photon particle** in the vacuum. ( J = 0 ).

In this case, the relativistic Lorentz gauge's fictitious electromagnetic equation becomes

*(Eq.6-6) Broken Maxwell equation by Lorentz gauge restraint in the electric current J = 0*

The broken Maxwell equation of Eq.6-6 clearly **disagrees** with the original Maxwell equation of the first line of Eq.6-5, but this broken Maxwell equation is the only choice for getting the photon's or vector potential A's wavefunction in the relativistic quantum field theory and QED.

The second-derivative ∂^{ν}∂_{ν} in the upper Eq.6-6 acting on the exponential function of photon A's wavefunction gives the relativistic energy equation with massless photon = Klein-Gordon equation with zero mass version ( this p.9, this p.3-4, this p.2, this p.9, this last, this p.6-7 ).

The most serious problem is this relativistic quantum field theory and QED using the quantized (unphysical) photons contained in the magnetic (or electric ) potential A can **Not** describe the ordinary constant magnetic field caused by the constant electric current J.

In Lorentz gauge or Coulomb gauge, the broken Maxwell equation consisting of the second-derivative with respect to the time and space allegedly gives the (virtual) photon's energy (= E ) and momentum (= p ).

In the constant magnetic field produced by the constant electric current, the time derivative giving the photon's energy E is zero (= due to the constant magnetic vertor potential A with respect to the time ), hence, the space derivative giving the photon's momentum p must be zero, too ( E = p = 0) in the vacuum, as shown in the above figure where the broken Maxwell equation's the second space derivative ∂^{2}A = p^{2}A = 0 becomes zero. ← the photon's momentum p (= expressed as the space derivative ) must be zero in the vacuum despite the existence of magnetic field.

But there is (constant) magnetic field in vacuum, which magnetic field has a power to push or pull the electric charge, which means the magnetic field must contain photons with some amount of energy and momentum (= photon's energy in the magnetic field vacuum should **Not** be zero ).

↑ As a result, the relativistic quantum field theory or QED giving the **false zero** photon's energy in the constant magnetic field is **wrong**.

The original complicated Maxwell equation like in the upper Eq.6-5 can **Not** be solved (= hence, photon A's wavefunction cannot be obtained in the original Maxwell equation ) using the following ordinary relativistic photon's solution or wavefunction,

*(Eq.6-7) Photon wavefuntion satisfying the broken Maxwell equation*

The fictitious photon's solution or wavefunction of Eq.6-7 satifies only the **broken** simple Maxwell equation of Eq.6-6, and does **Not** satisfy the original complicated Maxwell equation of Eq.6-5-upper.

↑ This means the fictitious photons used in the relativistic quantum field theory and QED **contradict** the experimentally-verified Maxwell equation of Eq.6-5-upper, so wrong.

These fictitious "photon particles" satisfying the broken Maxwell equation in relativistic quantum field theory or QED are just **nonphysical** math symbols (= ex. a photon is expressed just as a^{†} ) with No real figures ( this p.2-right, this p.3-7, this p.13-21 ).

*(Eq.6-8) Lorentz (= Feynman ) gauge compatible with relativity contains unreal time-like scalar photons with negative probability. ← Einstein relativity is false.*

To obtain the (broken) Maxwell equation of Eq.6-6 in the relativistic Lorentz or Feynman gauge conditions, it must always contain four types of (unrealistic) polarizations such as zero-polarized scalar ( time-like ) photon, x,y-two poralized photons, z-longitudinal photon ( this p.49 (or p.50), ).

To satisfy the superstitious Einstein relativity or Lorentz invariance condition, the sign of the zero-component (unreal) photon and the other three component photons must be the opposite.

↑ This relativistic unreasonable constraint generates the unreal zero component scalar (= time-like ) photon, which must have the unrealistic negative probability ( this p.10-(6.50), this 2nd-paragraph ) or norm ( this p.3-4, this p.4-left, this p.2-right-upper, this p.49-lower, this p.6-(6.34) )

As shown in the upper Eq.6-8, the number (= expressed as number operator N, this p.14 ) of this unrealistic zero-component scalar (= time-like ) photon in the relativistic QED magically **decreases** when this scalar photon is **created** by creation operator due to its extra minus sign (= a^{†}, this p.3-right, this p.100-last-paragraph ) which is contradictory and wrong.

But this contradictory zero-polarized scalar photon is indispensable for the relativistic QED calculation (ex. for anomalous magnetic moment ) to keep relativistically Lorentz invariant form ( this p.3 = Lorentz or Feynman gauge photon propagator including all four-component photons is used in QED, this p.8 ). → meaningless infinity in QED calculation.

Relativistic QED calculation uses unreal virtual photon propagator ( this p.3 ), which must include the unreal four types of polarized photons (= including unreal scalar zero-polarized photon ) as the form of the four-vector metric tensor = g_{μν} ( μ, ν, = 0,1,2,3, this p.6, this p.4~p.5-left-lower ) in calculating the anomalous magnetic moment.

So all the relativistic quantum field theory such as QED and standard model containing contradictory virtual and scalar photons with negative probabilities are illegitimate and **false**.

*(Eq.6-9) Relativity contradicts Maxwell equation, unless it imposes many artificial rules to destroy the original Maxwell equation.*

The important point is that Einstein relativity contradicts the experimentally-verified Maxwell equation, which proves Einstein relativity is false.

To artificially match (broken) Maxwell equation, physicists have to impose various aritificial rules such as Coulomb or Lorentz gauge conditions which break the original Maxwell equation even by creating the fictitious zero-component photon with unreal negative probability.

In order to obtain the Maxwell electromagnetic energy density in the vacuum, physicists have to **give up** Einstein relativity (= Lorentz invariance is violated, this p.5-upper ) and impose the contradictory Coulomb gauge condition.

Coulomb gauge has to often make the electric potential zero (= A^{0} = φ/c = 0, this p.4-(6.15), this p.3-lower ), which means the electric field (= E ) of the fictitious Coulomb gauge can Not be generated from the ordinary electric charge (= electric charge or electrons should generate electric potential φ, but these electric charges must be unrealistically zero in the ad-hoc Coulomb gauge ).

As a result, all the present relativistic and nonrelativistic quantum field theory, QED and standard model are based on contradictory concepts and artificial rules which cannot predict anything, so they are a useless and wrong theory.

2022/8/1 updated. Feel free to link to this site.