﻿ Special relativity with paradoxes is wrong.

# Einstein's special and general relativity is wrong due to its fatal twin paradox caused by fictional time dilation.

## Einstein rejecting real medium had to create paradoxical relativistic Lorentz transformation to explain the constant light speed c seen by any differently-moving observers.

### [ Michelson-Morley experiment showing the constant light speed c in any directions can be perfectly explained by the realistic medium or atmosphere moving with the Earth without fictional Einstein relativity. ]

(Fig.1) Light speed is always "c" in any observers moving at different speeds in any inertial frames. → Fantasy relativity and its Lorentz tranformation of spacetime.

(Fig.2)

Michelson-Morley experiment showed that light always travels at light speed c regardless of the Earth's direction.

Einstein relativity unscientifically dismissed the realistic medium or aether ( moving with the Earth ), so it had to create the paradoxical relativistic theory and its fictional Lorentz transformation of spacetime to explain why any observers moving at arbitrary velocities or any frames (= like the Earth moving around the Sun ) always see the constant light speed c.

↑ But actually, the light speed is slightly slower due to the atmosphere or air medium moving with the Earth, so Einstein relativity is based on the wrong postulate that the constant light speed c may not be affected by any medium.

Michelson-Morley experiment showing the constant light speed c (= a little slower due to the atmospheric air medium moving with the Earth ) measured in any arbitrary directions can be perfectly explained by the realistic medium moving with the Earth (= ether drag theory can perfectly explain stellear aberration ).

Einstein unscientific Lorentz transformation can be derived by the unrealistic postulate that the speed of the light emitted from the origin ( x=x'=0 ) at the time of t=t'=0 is always observed to be the constant light speed c seen by any differently-moving observers in both the static K frame and the K' frame moving in the x direction at a velocity of v.

(t,x,y,z) is the time (= t ) and space (= x ) coordinate of the static observer's K frame.
(t',x',y',z') is the time (= t' ) and space (= x' ) coordinate of the moving observer's K' frame which is moving at a velocity v in the positive x direction relative to K frame.

## Derivation of Einstein relativistic Lorentz transformation from the constant light speed c seen by any observers.

### [ An observer at rest in the rest frame K vs. an observer moving at a velocity of v with the moving frame K' ]

(Ap.1) K' frame is moving at a velocity v to the right (= in the plus x direction ) relative to the rest frame K.

We think about the case when an observer in K-frame is at rest, and another observer in K' frame is moving at a velocity of v in the right (= +x ) direction, and these two observers are supposed to see the same light and detect it as the constant light speed c (= as seen in Michelson-Morley experiment in the case of no medium ).

↑ From this (unrealistic) postulate, we can obtain the Einstein's relativistic Lorentz transformation formula of time (= t ) and space (= x, y, z ).

We suppose the time and space coordinate of K frame is expressed as ( t,x,y,z ), and the time and space of the moving K' frame is expressed as ( t', x', y', z').

At the time t = t' = 0, the coordinates of K and K' frames just overlap each other like (x,y,z)=(0,0,0)=(x',y',z')=(0,0,0).

At time t = 0 (= t' =0 ), the light is emitted from the source at the origin (= x = x' = 0 ).
( At time t = t' = 0, both origins x=x'=0 in K and K' frames are supposed to be in the same position. )

(Ap.2) Light speed is observed to be always constant "c" as seen by any observers in both the rest frame of K and the moving frame of K'.

After some time ( clock time of t in K frame when the clock time of t' in K' frame,  = these two clock times in different frames allegedly pass at different paces in the paradoxical relativity ), both observers measure the positions of light in each frame.

Though only K' frame is moving, and K frame is at rest, the light speed must be the same "c" from the viewpoints of both these differently-moving observers in K and K' frames, according to strange special relativity ( this p.18-19 ).

(Ap.3) Light speed is always "c" irrespective of observer's movement.

As a result, special relativity demands that both two equations of Ap.3 must hold at the same time.

In the upper Ap.3, when the measured time is t in K frame, the light has traveled the distance ct ( c is the constant light speed ), which means the traveling light's position (= x,y,z ) after the time of t has passed is expressed as x2 + y2 + z2 = c2t2 ( when t = 0, the light was emitted from the origin of x,y,z = 0,0,0 ).

When the measured time is t' in K' frame, the light has traveled the distance ct' ( c is the constant light speed ), which means the light position (= x',y',z' ) after the time of t' has passed is expressed as x'2 + y'2 + z'2 = c2t'2 ( when t' = 0, the light was emitted from the origin of x',y',z' = 0,0,0 ).

To satisfy these two equations of the upper Ap.3 demanded by Einstein relativity of constant light speed c in any frames, the space and time coordinates must transform like,

(Ap.4) Lorentz transformation of time (= t ) and space (= x,y,z ) between two frames K (= t, x, y, z ) and K' (= t', x', y', z' ).

According to the upper paradoxical Einstein's relativistic Lorentz transformation, the time (= t in K rest frame,  t' in K' moving frames ) and space (= x,y,z in K rest frame ,  x',y',z' in K' moving frame ) transform differently and unrealistically.

Because in the realistic (classical) world, the measured time must be the common concept ( t = t' ) of all differently-moving observers, irrespective of observers' motions, viewpoints or different frames.

And the coordinate x' in the K' frame moving at the velocity v in the positive x direction must be expressed as x' = x - vt (= x is the x coordinate of the rest frame K ), like

(Ap.5) Classical (= real ) vs. strange relativistic Lorentz transformation.

Of course, in the classical space time (= real world ) of the upper equation of Ap.5, the Einstein relativistic postulate of Ap.3 (= any differently-moving observers see the same constant light speed c even without the light medium ) cannot be satisfied,

(Ap.6) Classical (= realistic ) transformation of spacetime.

But of course, in this realistic classical mechanical space time, fatal paradoxes such as Twin paradox do NOT appear.

### [ Einstein relativistic Lorentz transformation satisfies the (unscientific) constant light speed c seen by any differently-moving observers. ]

(Ap.7) Lorentz transformation → constant light speed c in two different frames K at rest and the moving K'

(Fig.3) Light speed is always "c" in any frames under Lorentz transformation.

By inserting Einstein (unscientific) relativistic Lorentz transformation of Ap.5 into Ap.3, we know these equations are satisfied (= differently-moving observers in different frames K and K' magically see the same constant light speed c ).

## Relativistic Lorentz transformation causes fatal twin time paradox.

### [ Einstein fictional relativity with No absolute space or No absolute motion (= No absolute kinetic energy ) cannot explain even the actual simple phenomena where a moving electron loses its kinetic energy by emitting the light. ]

(Fig.4) K' is moving at v seen by the stationary K = the stationary K is moving in the opposite direction at -v seen by the moving K' = Which of K or K' is moving depends on observers = No absolute frame or No absolute motion in fantasied relativity.

In Einstein's paradoxical relativistic world, there is No absolute frame or No absolute motion (= hence, each particle has No absolute kinetic energy ). All things must be relative.

In the upper Fig.4-left, K' is moving at a velocity of v in the x direction seen by the stationary K observer.

But seen by the moving observer K', the stationary K is moving in the opposite direction at v, so which of K or K' is moving is uncertain and changeable depending on observers seeing it according to Einstein's paradoxical relativity.

This Einstein's No absolute frame (= No absolute motion or No kinetic energies ) causes the serious paradox, so the relativity is false.

For example, when an electron (= -e ) is moving at a velocity v (= which means this electron has kinetic energy of 1/2mv2 ), and losing its kinetic energies by radiating light seen by the stationary observer K, this moving electron appears to stop seen by the observer K' moving at the same speed as the electron.

↑ So when seen by the moving observer K', this electron appears to stop and have No kinetic energies which can be lost by emitting light energy, contrary to the stationary K observer seeing the electron moving (= having kinetic energy ) and losing its kinetic energy by radiating light energy.

Hence, whether this electron can lose kinetic energy by radiating light depends on which observer in the stationary K or the moving K frame is seeing the electron, this is clearly fatal relativistic paradox, because one observer can detect the emitted light recorded in the photodetector, while another observer cannot see the same photodetector detect the same emitted light.

↑ This Einstein relativistic paradox shows the amount of the particle's kinetic energy must be defined as how fast each particle is moving relative to some absolute frame or space medium where the emitted light wave (= Not unreal virtual photons ) is generated when the moving electron is losing its (real) kinetic energy.

We can exchange the K and K' coordinates ( t', x' ↔ t, x ), and replace v by -v (= the K appears to be moving in the opposite direction at v seen by K' ) in ordinary Lorentz transformation of

(Ap.8) ordinary Lorentz transformation

The coordinate in K' frame (= moving in the +x direction at a velocity of v relative to K ) is ( t', x', y', z' ), and K frame is ( t, x, y, z ).
The reverse Lorentz transformation of Ap.8 becomes

(Ap.9) reverse Lorentz transformation

The upper Ap.9 shows K (= whose coordinate is t,x,y,z ) appears to be moving in the opposite -x direction at a velocity of -v seen by K' (= whose coordinate is t',x',y',z' )

If you substitute Ap.9 into Ap.8, you can confirm these two relativistic Lorentz transformation formulas are right.

## Time dilation and twin paradox.

### [ Time of the clock moving with the moving frame K' (= this clock is fixed at x'=0 in K' frame ) ticks slower than the rest-frame clock K ]

(Ap.10) Time dilation of a moving clock K' relative to the stationary clock K.  Time t' in the moving K' frame is slower than the time t in the stationary K frame.

According to (illusory) Einstein relativistic world, the moving clock ticks slower than the stationary clock, which is clalled "time dilation ( this p.4 )", which has nothing to do with the (illusory) muon with higher energy able to travel longer.

But which clock is moving or stationary changes depending on which observer is seeing, which causes serious twin paradox about which clock time is slower.  ← This relativistic twin time paradox is a true paradox showing Einstein relativity is false.

So when K' is moving at a velocity v with respect to the stationary K, the clock time (= t' ) moving with K' frame (= this clock moving with K' is fixed at the origin x' = 0 in the moving K' coordinate ) appears to be slower than the stationary K clock time (= t,  this p.20 ),  like

dt (= faster time in K ) > dt' (= slower time in K' ).

Substituting "x' = 0 (= a moving clock fixed in the origin of the moving frame K' )" into the first equation of Ap.9 (= Lorentz transformation of time seen by the stationary observer K with clock time t ), you can get the delayed moving clock's time relative to the stationary clock of upper Ap.10 result.

It means the time dt' measured in the clock K' moving at v is slower and delayed compared to the time dt measured in the stationary clock K ( this p.2-3,  this p.18,  this middle ).

### [ Moving clock "always" ticks slower. → Twin paradox about which clock ticks slower. ]

(Ap.11) Time dilation of a moving clock K seen by K'.

But from the view point of the moving K', the stationary K clock appears to be moving in the opposite -x direction at a velocity -v, hence, this K clock appears to be moving and ticking slower than the K' clock like ( this p.2-time dilation,  this-(1)-(4) )

dt (= slower time in K ) < dt' (= faster time in K' ), when we insert x = 0 (= K clock is fixed at x = 0 in K frame ) into Lorentz transformation equation.

dt > dt' and dt < dt'  which is clearly time paradox called twin paradox, which is a true unsolved paradox.

## Twin paradox --- Which clock runs slower ?

(Fig.5) Which clock ticks more slowly ??

The results of Ap.10 and Ap.11 show which clock of K or K' ticks slower is paradoxical (= each observer always sees the other observer's clock ticking slower, hence, both clocks of K and K' tick slower, which is paradox ), this means Einstein relativity is false.

## Gravitational time dilation by general relativity is unreal.

### [ Clock ticks slower at points nearer to the mass (= like Earth ) with greater gravity ? ]

(Fig.6) Clock time (= t0 ) nearer the Earth with mass M is slower than the clock time (= tf ) distant from the Earth with No gravity ?

Einstein general relativity claims the clock time nearer to the Earth with mass M is slower due to greater gravity ( this middle,  this p.15 ).

Time t0 at a point which is separated from the Earth's center by the distance r is expressed like the upper Fig.6 using the gravitational potential (= -GM/r,  this p.5 ).

The point is this gravitational time dilation is simple, which depends only on the distance (= r ) between the clock's position and the Earth's center or gravitational potential (= other factors such as the gravitational constant G, the Earth's mass M, the light speed c are the constant fixed values ).

It means two satellites moving around the Earth in the same orbit (= the same orbital radius is r, hence, No gravitational time dilation difference ) in the opposite directions face the fatal twin paradox where each satellite always see the other satellite moving, and, which satellite's clock ticks slower becomes paradoxical due to special relativistic time dilation of moving clocks.

Einstein relativistic time dilation disagrees with the experimental results, as seen in the fact that GPS satellite clock time error (= caused by discrepancy between actual GPS time and the theory ) must be constantly corrected by directly comparing GPS time and the ground station's time.

The areas with different gravitational forces are completely different circumstances with respect to the atmospheric pressure and temperature, and the light speed c is known to become slower to c/1.0003 due to the air medium on the Earth, which medium's influence on the light wave is far stronger (= light speed c is modified into c/1.0003 where 1.0003 is the refractive index of air, which influence is as large as 10-4 ) than the dubious extremely-weak gravitational time dilation (= which dubious gravitational time dilation influence is far smaller = only 10-15 than the air medium = 10-4 ).

Hence, it is natural that not only light speed c, but also the light frequency, atomic motion and atomic clock time are also slightly modified in completely-different circumstances with different gravitational force = different atmospheric pressure, which has nothing to do with Einstein paradoxical time dilation.

## GPS clock gains time of 38 microseconds per day due to Einstein relativity ?  ← This is wrong because it includes twin paradox of special relativity !

### [ GPS clock ticks faster by 45 μs due to weaker gravity (= smaller general relativistic time dilation ) and ticks slower by 7 μs due to the faster-moving satellite (= special relativistic time dilation causing twin paradox ! ), hence, GPS clocks runs faster by 45-7 = 38μs per day ? ]

(Ap.12) Einstein relativistic time dilation in GPS ?

The actual GPS satellite's atomic clock completely disobeys Einstein relativistic time dilation, so GPS clock causes many unpredictable errors which must be constantly corrected by the ground station's clock.

But the textbooks often use the misleading case of a GPS satellite moving at a velocity of 14000 km/hr (= 3889 m/s ) at an altitude of 20000 km, so the satellite's distance from the Earth center is r = 20000km + 6378 km (= Earth's radius R ).

This satellite's clock is said to run faster than the Earth's clock by 45 microseconds per day because the gravilatioal time dilation is weaker at the higher altitude (= greater distance r = 26378 km from the Earth center ) than the Earth's surface (= distance from the Earth center is Earth's radius = 6378 km ).

And this satellite's clock is said to run slower by 7 microseconds (= μs ) per day because the satellite is moving faster (= satellite's speed is about 14000 km/hr = 3889 m/s ) than the Earth's surface (= Earth rotation speed is 1670 km/hr = 464 m/s ).

Hence, the satellite's clock is said to run faster by the total 45 μs - 7 μs = 38 μs than the clock on the Earth's surface per day ( this p.23-24 ) .

But as I said, this GPS time special relativistic time dilation allegedly caused by moving clocks cannot avoid the fatal twin paradox, so Einstein relativity is false.

(Ap.13) GPS satellite cannot avoid fatal twin time paradox, so Einstein relativity is false.

## Lorentz contraction. = Even rigid body must be contracted just by observer's movement according to fictional Einstein relativity.

(Ap.14) Moving objects are contracted ?  → paradox.

According to the paradoxical Einstein relativity, the moving object must be contracted and shortened, even if it is an extremely hard rigid object.

This is called Lorentz contraction which also causes serious paradox like twin time paradox.

(Ap.15) Lorentz tansformation.

We use the basic relativistic Lorentz transformation to derive this supernatural phenomena called Lorentz contraction.

(Ap.16) Stick is moving with K' frame at velocity "v" relative to K.

In the upper Ap.16, a stick whose length is l0 is moving at a velocity of v in K' frame relative to a stationary observer in the rest frame K (= this stick of length l0 is at rest relative to the moving frame K', and moving relative to the rest frame K ).

At time "t", both ends of this stick are at x2 and x1 in K frame.
So the length of this stick in K frame is l = x2 - x1.

The length of the object means the value measured at the same time "t".
Using Lorentz transformation of Ap.15, x' coordinates ( in K' frame ) of both ends of the same stick are

(Ap.17)

Considering the rest length of this stick is l0 = x'2 - x'1 (= this stick is at rest in K' frame, so the coordinates of this stick's both ends x'2 and x'1 are the fixed values irrespective of the time t or t' ),
(Ap.18)

As shown in the upper Ap.18, the moving object must become contracted in the moving direction according to Einstein Lorentz transformation and contraction.
( The length of the moving stick as seen by K frame observer looks shorter than the original rest length l0 seen by K' frame observer. )

This occult phenomenon is called "Lorentz contraction" where moving objects appear to be contracted in the moving direction seen by stationary observers (= but as I said, which observer is moving or stationary is relative, Not absolute, so which stick is contracted causes serious paradox like twin time paradox ).

(Ap.19) Lorentz contraction is "real" ?

As shown in the upper Ap.19, the object whose length is l0 must appear to be contracted and shortened to the length l (< l0 ), when this object is moving.

Of course, this magically contracted object cannot be detected in actual experiments.

## Relativistic Lorentz contraction causes fatal Ehrenfest paradox, so false.

### [ Special relativity can NOT deal with two directions. ]

(Ap.20) Which is the true circumference of disc ??   → Paradox !

In the upper Ap.20 the circumference of the round disc is 2πR ( R is radius ).
And this 2πR is just equal to N × l0 in the stationary disc of Ap.20 left. ( 2πR = Nl0. )

When the disc starts to rotate, its circumference becomes Lorentz- contracted, because rotation means the movement in the tangential direction (= all stick or circumference must be shortened or contracted in the moving tangential direction according to Einstein Lorentz contraction ).

But the radius "R" is NOT Lorentz contracted, because there is no radial motion. ( R → R )

Considering each length l0 of this rotating disc is contracted, its circumference is NOT equal to 2πR. ( 2πR < Nl0 ? )

↑ So the length of the circumference of the rotating disc is uncertain and paradoxical about whether the circumference is 2πR (= radius R is Not Lorentz contracted ) or less then 2πR (= due to the circumference must be Lorentz contracted in tangential (= rotating ) direction ).

This is one of fatal paradoxes of special relativity. (= Ehrenfest paradox. )
Even if the rotating "rigid" disc is broken, each crack of it is also contracted, so this broken disc cannot solve this paradox.

Unfortunately, these "real" paradoxes can NEVER be found in ordinary relativity textbooks. Why?
( Caution: observer A is stationary existing in the stationary hole at the center of this disc, so various general relativistic effect such as centrifugal potential has nothing to do with it, and only special relativistic Lorentz contraction needs to be considered, and causing this unsolvable Ehrenfest paradox )

## Special relativity contains serious "paradoxes".

(Fig.7) Fatal paradoxes → special relativity is wrong.

This Lorentz transformation causes serious paradoxes such as Electromagnetism and Right-angle lever.
Unfortunately, these paradoxes have NOT been solved.

When you see various solutions to these paradoxes, you find they are ad-hoc and based on wrong assumptions.

## True paradoxes are hidden from ordinary people.

(Fig.8) Journals, universities, textbooks .. are hiding true paradoxes from students.

When you see various textbooks, journals, websites of universities, and other media, you notice Only "fake" paradoxes such as ladder paradox and twin paradox are shown.

True paradoxes such as Lorentz force and right angle lever cannot be seen at all.
( Or they are put in the shade, inconspicuous places. )

As far as they continue hiding these true paradoxes, students and ordinary people will be deceived and their precious future will be jeopardized.

## Special relativity needs many kinds of "ether" !?

(Fig.9) Ether was denied. → dark energy, matter, Higgs = ether revived !?

It is said that special relativity denied luminiferous ether.
But instead, they needs many kinds of matters filling all space, such as dark matter, dark energy, Higgs, and virtual particles.

So, the kinds of ether-like matters are increased in special relativity !

If we accept only one kind of realistic "medium", we can naturally explain dark matter, uniform CMB, without depending on virtual particles violating relativity.

## Faster-than-light inflation is indispensable for relativity.

(Fig.10) Faster-than-light inflation = special relativity !?

Surprisingly, because special relativity denied aether, the current physics demands faster-than-light cosmic inflation.

To explain the uniformity of microwave background even in superluminal regions, space must have expanded with superluminal speed, physicists insist.

But as you feel, these explanations are completely inconsistent with the heart of special relativity, which claims any objects cannot exceed the light speed.

## "Ether (= or realistic medium )" moving with the earth is realistic.

(Fig.11) Michelson-Morley experiment = "ether" moving with the earth ?

In Michelson-Morley experiment, they tried to observe the electromagnetic wave's interference changes.
( So the light speed "c" depends on the wave nature of the light. )

The earth is moving around the sun.
So if some medium (= ether ) fills the absolute space, "ether wind" is blowing in the opposite direction to the earth's movement, which would cause light interference changes.

But there were no interference changes in the various directions in this experiment.
Ordinary relativity textbooks often say this experiment denied the "ether" (= ether wind ).

(Fig.12) All charges are moving with earth !

If the ether is moving with the earth like the air and all other things, the speed of light is always constant "c", NOT causing "ether wind".

And all charged particles including our human bodies are moving with the earth, and it is natural to think the electric field E among them is moving with the earth.

The velocity of the electromagnetic waves completely depends on some medium such as air and water moving with the earth.

## Relativistic quantum field theory accepts "ether wind" !

(Fig.13) Relativistic quantum field theory accepts "ether wind" !

When most people hear the word of "ether", they blindly reject the idea without thinking deeply.
But as I said above, the present quantum field theories such as QED and standard model use various kinds of "ether" like matter.

If you reject the "ether", you have to use infinite virtual particles to express the Coulomb and magnetic forces, which fill all space.   These virtual particles do NOT obey special relativity (= Einstein formula ).

And other things such as dark matter, dark energy and Higgs field also fill all space.
But they try NOT to admit these "ether-like" things are ether, because they are "relativistic" quantum field theory.

And they are doing just "Shut up and calculate !" about the present particle physics.
( These contradictory ideas clearly obstruct the develop of science of our human beings. )

## Fatal paradox of "contracted" conveyor belts.

(Fig.14) "Lorentz-contracted" conveyor belt. ← Paradox !

The upper Ehrenfest paradox can be easily imagined using conveyor belt.
In Fig.14 left, a conveyor belt is not moving.

If you rotate this conveyor belt, this belt becomes Lorentz contracted according to the special relativity ( Fig.14 right ).

So the whole length of this belt becomes contracted !
This is clearly a fatal paradox, because inner square frame is not moving and keep the same length.

## Weak points of special relativity is two directions.

(Fig.15) Two directions = weak point of relativity.

In conclusion, the fatal paradoxes of special relativity appear when we try to deal with two directions.
Two directions ( r and θ, x and y, circular wire ) are weak points of the special relativity.

And all people involved in physics education carry grave responsibility for teaching something related to relativity to students, hiding its fatal paradoxes.
( Includig QED, standard model, general relativity, and relativistic quantum chemistry. )

Because they damage the student's precious future by teaching paradoxical relativity.

## Muon lifetime does NOT mean special realtivity.

(Fig.16) Who ordered the muon ?

It is natural that we think the lifetime of the muon becomes longer (= a particle can move longer distance ) due to its higher energy itself NOT by strange time dilation.

Unnecessary and unstable elementary particle muon is thought to be a combination of electron and high-energy de Broglie wave (= neutrino ).
Because the neutrino can penetrate the earth easily.

## Fizeau experiment did NOT deny "earth ether".

(Fig.17) Fizeau experiment and aberration denied ether dragging ?

Fresnel's theory of aether dragging was confirmed by Fizeau experiment in 1851.
In this experiment, the moving water "partially" dragged the light (speed), as shown in Fig.42A.

Relativists often insist that this experiment denied the complete aether dragging theory.
But as you notice, their insistences neglect the power difference between the very "small" water and very "big" earth, and the relation between the medium motion and its refractive index change.

## Special relativity cannot explain why light becomes slower in water (= medium ).

(Fig.18) Photon can NOT be slower in the water.

According to the relativity, when the particle with some mass is moving at the light speed c, its energy E becomes divergent to infinity ( Fig.18 upper ).
So the photon's mass must be zero.

If the photon's speed becomes slower to c/n in the water, its energy E becomes zero, because photon has no mass. ( Fig.18 lower. )
Of course, this is inconsistent with the photon's energy E = hν.

As a result, the relativity does NOT allow the photon to be slower than "c".
And the relativists often insist Fizeau experiment shows the Lorentz transformation.

But admitting "c/n" speed in the water means the light speed completely depends on the medium.
( "n" is the index of refraction for water = 1.33. )

## Aberration can be explained by "ether dragging" or the medium moving with the earth.

### Einstein relativistic theory rejecting real medium in space turned out to be wrong.

(Fig.19) Star's light moving at slightly tilted angle by the earth motion generates "ripple" when it hits the earth medium, causing "aberration" or the light traveling at the tilted angle.

The mainstream explanations about aberration using ether drag are often based on wrong assumption that the medium dragged by (= moving with ) the earth is falsely treated as "solid" rebounding the star's light particle without generating ripples.

As shown in the upper figure, from the viewpoint of the earth, the star's light is traveling in the outer-space medium slightly tilted at an angle (= tan θ = v/c where c is light speed ) by the earth moving at speed of v.

So from the viewpoint of the medium moving with the earth at a speed v (= corresponding to dragged ether ) relative to the outer-space medium, the star's light traveling in the outer-space medium has the tilted momentum (= at an angle of θ ), as shown above.

When this star's light with the tilted momentum hits the earth medium (= medium moving with the earth ), it generates a light ripple tilted at almost the same angle in the earth's medium, hence, the aberration (= tilted light by the earth movement ) can be observed also in the medium or ether-drag theory.

## Ether drag or medium theory can explain aberration using also Snell's light refraction law.

(Fig.20) Snell's law can explain aberration in the light medium moving with the earth.

We can explain why the aberration can be observed also in the medium or ether-drag theory using the classical Snell law of light refraction.

According to Snell law, the angle (= θ ) at which the light is tilted depends on the light speed (= v1 and v2 ) in each medium.

In this case, the earth's speed v is much lower and slower than the light speed c, hence, we can think the light speeds in the outer space medium and the medium moving with the earth are almost the same c (= v1 = v2 = c ).

It means the light tilted at an angle of θ1 in the outer space keeps almost the same angle (= θ2 = θ1 ) also in the earth's medium, and the tilted light or aberration can be observed also in thie medium theory.

## Transverse Doppler effect by "classical" mechanics.

(Fig.21) Transverse Doppler effect.

It is said that "transverse" Doppler effect cannot be explained by nonrelativistic effect.
But is it really so ?

Due to time dilation of moving object (= light source ), its original light frequency becomes lower at the stationary observer, they insist.

(Fig.22) Transverse Doppler effect = time dilation !?

In Fig.21,22, the light source is moving to the right at the velocity v, and emits the light upward when it just passes the observer.
As I said above, the clock with moving object (= K' light source ) ticks slower than K frame clock.

(Fig.23) Original light frequency (= ν0 ).

During the time of dt', the number of emitted light (wavelengths) from the source is dn'.
So the light frequency in K' frame is ν0 = dn/dt'.

(Fig.24) Observed frequency (= ν' ) becomes lower than ν0.

While the time dt' has passed in K' frame, the time dt has passed in K frame. ( dt > dt' due to time dilation )
As a result, the observed light frequency in K frame becomes lower, because dt is bigger than dt' ( "dn" is the same ).
So they insist this transverse Doppler effect is caused by the time dilation.

But from the viewpoint of the light source, K frame observer is moving ( dt < dt' ) , so this result becomes opposite (= twin paradox ). This is strange.

As a result, transverse Doppler effect has nothing to do with time dilation and relativity.

## Transverse Doppler effect by classical mechanics.

(Fig.25) Transverse Doppler effect by classical mechanics.

Instead of using this "strange" time dilation, we can describe this effect by "classical" method.
As shown in Fig.25, due to the movement of the light source, the emitted electromagnetic wave (length) is elongated.

As a result, the observed light wavelength λ' is elongated like,
(Fig.26)

The frequency is inverse proportion to the wavelength.
So the observed light frequency (= ν') becomes

(Fig.27) Observed frequency (= ν' ) becomes lower than ν0 also in classical picture.

Fig.27 is equal to Fig.24.
So we can explain transverse Doppler effect by the classical electromagnetic wave.

As you notice, the result of Fig.25 and FIg.27 show intermediate frequency between the frequency of the light coming toward us and that of the light going away, because it's "transverse" direction.

If you insist that the transverse Doppler effect is due to purely relativistic effect, you need to use a photon particle, because the relativity is using virtual photons as Coulomb force.
But basically it is very strange that we think the "photon particle is oscillating" at the frequency ν0.

## "Mass" cannot be converted into other energies.

(Fig.28) Even when we break mass into pieces, total mass remains the same.

The current relativistic quantum field theory claims the rest mass of an electron and its (unrealistic) antiparticle positron could change into a light or photon with zero mass, but this explanation is intrinsically impossible.

Because even if you can break the mass of some particle (= m ) into ( infinitesimal ) pieces, total mass remains the same (= m ).

So the idea that mass can be changed into light with no mass is impossible.

## Four momentum = relativistic momentum and energy.

Dirac equation is indispensable for QED, standard model and string theory.
Here we show that Dirac equation uses relativistic momentum and energy (= four vector momentum ).
And these four momentum causes fatal paradox of right angle lever paradox, which means all these relativistic quantum field theories are wrong.

### [ Proper time is Lorentz invariant. ]

In the relativistic theory, clocks tick differently depending on their frames.
So it is useful to introduce some new concept of time, which is invariant under Lorentz transformation.
This is called "proper time" ( τ ).
(Eq.1)

In Eq.1, "u(t)" is the object's velocity in K frame, an "t" is the time in K frame.
( In special relativity, the velocity becomes different in different frames. )

The proper time is the time which is measured in system of coordinates moving along with the object.
So this proper time does not change under Lorentz transformation (= Lorentz invariant ).

From Eq.1, the proper time is
(Eq.2)

Eq.2 is Lorentz invariant scalar like
(Eq.3)

We can treat this proper time as a "constant" under Lorentz transformation.
(Eq.4)

Considerting Eq.3 and Lorentz transformation, the special relativity defines four vector as
(Eq.5)

### [ Relativistic energy and momentum. ]

As I explain later, the relativistic mass of a moving object is heavier according to the special relativity.
So the relativistic momentum (= p ) can be expressed as
(Eq.6)

Eq.6 can be expressed as
(Eq.7)

From Eq.5-Eq.7 (= proper time), the denominator of Eq.7 can be considered as a constant.
So Eq.7 changes as x compoment of the four-vector under Lorentz transformation.

Replacing x by ct (= zero component of the four-vector, see Eq.5 ), Eq.7 becomes
(Eq.8)

From Eq.8, we can define the zero component of the four vector, as follows,
(Eq.9)

where E is the relativistic energy of
(Eq.10)

Here we use the notation, p0 = - p0.
As you see the derivation of Eq.17, these relativistic momentums transform like spacetime ( ct, x, y, z ) under Lorentz transformation.
So these are called "four-momentum".
(Eq.11)

As you see, these relativistic momentum and energy satisfy the following important equation,
(Eq.12)

The important point is that Eq.12 does NOT change under Lorentz transformation (= scalar ).
In the quantum mechanics, the relativistic energy (E) and momentum (p) are replaced by the operators like
(Eq.13)

Using Eq.13, Eq.12 can be expressed as
(Eq.14)

where φ(x) is called Lorentz scalar field (= Klein- Gordon field ).
So Klein-Gordon (K-G) equation is just equal to special relativity.
For φ(x) to be scalar, this φ needs to include infinite kinds of momentums, which lead to ultraviolet divergence

As shown on this page, Dirac equation can be gotten from Klein-Gordon equation.
So Dirac equation itself is just equal to the special relativity.
Dirac (or K-G) equation uses the time and space coordinates ( = kx ) as four vector, which is based on the special relativity (Eq.24).
(Eq.15)

If the faster-than-light neutrino is correct, this means the Dirac equation and the special relativity are wrong.
If so, all other relativistic theories (= QED, standard model, string theory ) using Dirac equation, are all wrong.

## Four velocity and another methods.

### [ Another method and four-vector velocity. ]

Next we try another method to get the relativistic momentum and energy.
We define " four-vector velocity " (= ω ) , as follows,
(Eq.16)

where the proper time (= τ ) is Lorentz invariant, so Eq.16 change as four-vector such as (t, x, y, z) under Lorentz transformation.

From here, we use the next notation of
(Eq.17)

i = 1, 2, 3 components of four-vectors are
(Eq.18)

where Eq.1 is used.

And ω0 becomes
(Eq.19)

(Eq.20)

where g (or η ) means Minkowski metric tensor of
(Eq.21)

Using μ = 0, 1, 2, and 3, Lorentz transformation can be expressed as
(Eq.22)

where Loretnz matrix is
(Eq.23)

Eq.22 means
(Eq.24)

As a result,
(Eq.25)

So we can get the relation of
(Eq.26)

### [ Relativistic equation of motion. ]

Here we define new equations of
(Eq.27)

Using Eq.18 and Eq.19, we can get
(Eq.28)

When we use the same variable twice (like μ μ ), this means the sum of 0-3 components.

We differentiate Eq.28 by the proper time ( τ ), and divide it by 2,
(Eq.29)

where Eq.27 is used.

We introduce the new variable ωμ(τ) and fμ(τ) irrespective of reference frame.
So the next relation is naturally satisfied.
(Eq.30)

As shown in Eq.16, ωμ(τ) change as four-vector. So if fμ(τ) also change as four-vector,
(Eq.31)

We can get Eq.30.

So fμ(τ) of Eq.27 also change as four-vector like ωμ(τ).
We call these fμ(τ) " four-vector force ".

Here we define f i (τ) (i = 1, 2, 3 ) as
(Eq.32)

where F means Newtonian force.
This definition of Eq.32 is "artificial" to get the relativistic momentum.

And substituting Eq.18, Eq.19 and Eq.32 into Eq.30,
(Eq.33)

From Eq.33, the solution of 0 component ( = f 0 (τ) ) becomes
(Eq.34)

Using Eq.1, Eq.16 can be expressed as
(Eq.35)

Substituting Eq.18 and Eq.32 into Eq.35, we can get the equation of motion of
(Eq.36)

So we get the relativistic momentum ( = p ), as follows,
(Eq.37)

And substituting Eq.19 and Eq.34 into Eq.27,
(Eq.38)

So we get the relativistic energy ( = E ), as follows,
(Eq.39)

These results are the same as the upper section.
As I said, the definition of Eq.32, which represents the relation between Newtonian force F and the four-force, is artificial to get the relativistic momentum.
And this causes right-angle lever paradox, which rotation shows the weak point of the relativity.

### [ Four current density. ]

According to Maxwell's equation, the current density (= J ) and charge density (= ρe ) satisfy
(Eq.40)

Of cource, the total charge is conserved irrespective of reference frame,
So the equations of Eq.40 must be Lorentz-invariant.

But this definition of Eq.40 causes the violation of the total charge in the electric wire, as shown on this page !
This means the special relativity (= Lorentz transformation ) itself is wrong.
So we have to admit "ether" which is moving with the earth. (In this case, we don't need to use the relativistic restriction, because Lorentz transformation itself doesn't exist. )

Eq.40 can be expressed using four vector ( xμ ), as follows,
(Eq.41)

ct can be replaced by x0
And if we define the new four vector (= four current density ), as follows,
(Eq.42)

Eq.41 can be expressed as
(Eq.43)

Using Lorentz transfomation, the differentiation by xμ is
(Eq.44)

Substituting Eq.44 into Eq.43, we have
(Eq.45)

As a retult, Eq.43 (= Eq.40 ) proves to be Lorentz invariant.

2022/11/23 updated. Feel free to link to this site.