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Strange spin

Paradox of Lorentz force.

No solution.
Right angle lever.

Special relativity "really" ends. (14/ 7/21)

- What is special relativity ?
- Fatal paradoxes of special relativity.
- Antiparticles do NOT exist.
- Relativistic momentum and energy.

*(Fig.1) Light speed is always "c" in any inertial frames. → Relativity. *

Special relativity (SR) is the physical theory dealing with spacetime transformation proposed in 1905 by Albert Einstein.

Theory of relativity is so mysterious and there are many objections to this theory.

As shown in Fig.1, in the special relativity, the speed of light is **always** "c" from the viewpoint of any observers moving at **arbitrary** speeds.

To satisfy this **unrealistic** condition, the time and space are contracted or **dilated** like "fantasy".

*(Fig.2) Ball speed looks different depending on observer's velocity.*

In Fig.2, a ball is moving at a velocity "**V**".

Accoding to ordinary classical mechanics, when the observer is *moving* at a speed "*S*" in the same direction, the speed of the ball looks " **V** *- S* ".

*(Fig.3) Light speed is always "c", irrespective of the observer's speed ? *

Accodding to special relativity, the speed of light is the **same** for all observers,
**irrespective** of whether the observer is moving or stationary.

So the speed of light **always** looks "**c**" from the observer's viewpoints, both in Fig.3 right and left.

As I say later, if we assume the **ether** moving with the earth, we can naturally explain this constant speed "c".

*(Fig.4) K' frame is moving at velocity "v" to the right along x axis.*

At time **t = 0** ( t' = 0 ), the origins of K and K' frames **overlap**, and the light is **emitted** from the light source at the **origin**.

K' frame is moving in the positive x direction at velocity "**v**" relative to K.

At time **t = t** ( t' = t' ), observers in both K and K' frames **measure** the position of lights.

According to special relativity, in **both** frames ( rest and moving ), the light speed must be constant "c", so the following equations are satisfied.

*(Fig.5) In both frames, the light speeds are constant "c". *

As you see Fig.4, x' coodinate is moving relative to x. ( x' = x - vt )

So within ordinary classical mechanics, it is **impossible** to satisfy both equations of Fig.5 at the same time.

To do so, we have to accept the **strange** idea that the time and space are contracted or dilated by observer's movement (= Lorentz transformation ).

*(Fig.6) Light speed is always "c" in any frames under Lorentz transformation. *

If the time and space coodinates transform like Fig.6 in K and K' frames, both two equations of Fig.5 hold.

But of course, changing basic idea about spacetime **distorts** other basic physical principles.

About the caluclation, see also this section.

*(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.

*(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**.

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

As shown on this site, 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 ether, we can naturally explain dark matter, uniform CMB, **without** depending on virtual particles **violating** 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.

*(Fig.11) Virtual photon = tachyon !? → special relativity is wrong.*

In the relativsitic quantum field theory, virtual particles always appear in Feynman diagram.

As shown in this site, it is known that these virtual particles **always** violate special relativity.

But ordinary people do **NOT** know this important fact and they are **deceived** by various media and textbooks.

Special relativity insists Coulomb force is caused by exchange of these **virtual** photons.

For energy and momentum to be conserved, this virtual photon must be tachyon, as shown on
this page.

In conclusion, special relativity contains **self-contradiction** from the beginning, which means special relativity is **wrong**.

*(Fig.12) Influential Special relativity is used in various fields.*

Special relativity was introduced by Einstein a very long time ago in 1905.

So this idea was used in various relativistic theories such as standard model, QED, black hole, expanding universe and string theory.

If special relativity is wrong. **all** these theories would **break** down.

This is the main reason why physicists aim at various **fantasy** such as **10-dimensional** string theory and **superluminal** inflation even now, though they are clearly **fantasy**.

*(Fig.13) 26 → 10 dimensional string theory is left as the ONLY unified theory.*

As a result, as long as physicists believe special relativity, **ignoring** true paradoxes, 10-dimensional string theory is left as the **only** unified theory.

This means, the instant new students start to **doubt** "fantasy" string theory, they can **NEVER** advance in their physical careers. This is **disaster**.

*(Fig.14) Mathematical trick = Change of variable. QED is wrong.*

As shown on this page, the calculation of magnetic moment g-2 by quantum electrodynamics (= QED ) depends on **wrong** math tricks.

In Fig.14, "change of variables" ( k = l - β ) **artificially** changed the result itself.

This one-loop correction is ultraviolet **finite**.

In **two-loop** correction, even after ultraviolet (= UV ) divergence is renormalized, complicated infrared (= IR ) divergence is left.

As shown on this site (p.25-), the manipulation of infrared divergence is much more **difficult** than
UV divergence in higher-order correction. ( There is **NO** universal rule in removing IR. )

As many as eight years after one-loop calculation, they introduced various **artificial** new concepts such as modified propagator, Yennie gauge, and contact term to **adjust** them to experimental values.

( See "Particles. Sources, and Fields" vol 3, Schwinger )

So the loop corrections of anomalous magnetic moment are **NOT** natural results, at all.

*(Fig.15) QED cannot predict Lamb shift at all. *

In Lamb shift calculation, they **artificially** divided calculation into high and low energy terms to avoid **infrared** divergence.

But high energy term contains **virtual** photons, and low energy terms contain **real** photon.

So basically it is **unreasonable** to recombine relativistic and nonrelativistic terms. ( See "advanced quantum mechanics", JJ. sakurai )

Furthermore, we have to depend on **numerical** ( NOT analytic ) calculations and **virtual** excited states to get proper Lamb shift values.

( See this site (p.23) and The Quantum Theory of Fields, vol 1 p.592, Weinberg. )

So Lamb shift by QED is **NOT** first-principle, either.

*(Fig.16) 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.17) 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.

*(Fig.18) 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. )

*(Fig.19) Moving objects are contracted.*

In Fig.19, the original length of stick at rest is " **l _{0}** ".

After it starts to move, it appears

*(Eq.1) Lorentz tansformation.*

In Fig.20, there is a stick which rest length is **l _{0}**.

This stick is moving with K' frame at speed "v" relative to K frame.

So in K' frame, this stick is at rest, and its both ends are

*(Fig.20) Stick is moving with K' frame at velocity "v" relative to K.*

At time "**t**", both ends of this stick are at x_{2} and x_{1} in K frame.

So the length of this stick in K frame is **l = x _{2} - x_{1}**.

The length of the object means the value measured at the **same time** "t".

Using Lorentz transformation of Eq.1, x' coordinates ( in K' frame ) of both ends are

*(Eq.2)*

Considering the rest length of this stick is l_{0} = x'_{2} - x'_{1},

*(Eq.3)*

As shown in Eq.3, the **moving** object becomes **contracted** in the moving direction.

( The length as seen by K frame observer looks shorter than the original rest length l_{0}. )

This is called "**Lorentz contraction**".

*(Fig.21) Lorentz contraction is "real" ?*

According to the special relativity, Lorentz-contracted length of the object is treated as "**reality**".

In Fig.21 the object with a rest length of l_{0} is moving at speed "v" with respect to K frame.

And a lot of cameras are put along the wall of K frame, they take a snapshot of the object at the same time of "t".

In these pictures, the object length is always "**l**", not "l_{0}" according to the special relativity.

Though this measurement is **so** difficult that there has **never** been any direct test of length contraction, as shown on this site.

*(Fig.22) Which is the true circumference of disc ?? → Paradox ! *

In Fig.22, the circumference of the round disc is **2πR** ( R is radius ).

And this 2πR is just equal to N l_{0} in the stationary disc of Fig.22 left. ( **2πR = Nl _{0}**. )

When the disc starts to rotate, its **circumference** becomes Lorentz-**contracted**, because rotation means the movement in the **tangential** direction.

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

Considering each length l_{0} of this rotating disc is **contracted**, its circumference is **NOT** equal to 2πR. ( **2πR < Nl _{0}** ? )

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. This is strange.

Unfortunately, these "**real**" paradoxes can **NEVER** be found in ordinary relativity textbooks. Why?

( Caution: observer A is in the **stationary** hole at the center of this disc, so centrifugal potential (= general relativity) has nothing to do with it. )

*(Fig.23) "Lorentz-contracted" conveyor belt. ← Paradox !*

The upper Ehrenfest paradox can be easily imagined using **conveyor belt**.

In Fig.23 left, a conveyor belt is not moving.

If you **rotate** this conveyor belt, this belt becomes **Lorentz contracted** according to the special relativity ( Fig.23 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.

*(Fig.24) Belt is contracted or not, depending on observer's motion. *

As I said above, the **moving** object appears **shorter** from the perspective of a stationary observer.

Even when the observer starts to move relative to the belt, its length appears contracted.

*(Fig.25) The relation between belt's length and observer's motion.*

In Fig.25 left, conveyor belt is **moving** relative to the observer in **K** frame.

So in this case, moving conveyor belt is Lorentz-**contracted**.

When the observer starts to move at the same velocity as the belt, the belt looks **stationary** from that observer's viewpoint (= K', Fig.25 right ).

In **K'** frame, the length of belt **at rest** returns to the original, and becomes **longer** than that of K frame.

*(Fig.26) Inner frame becomes shorter in K'. *

On the other hand, the inner frame is at rest in K.

So while the observer is moving (= K' ), this inner frame becomes **contracted**.

Because from the viewpoint of K' observer, the stationary frame is **moving** in the opposite direction.

*(Fig.27) Belt is "separated" from inner frame by observer's movement ?? *

From Fig.25 and Fig.26, these conveyor belts and inner frame become **separated** due to their different total length.
This is very strange.

*(Fig.28) Horizontal wires ( at detector ) become 5 → 3 by observer's movement ? *

In Fig.28 left, the inner frame is at rest, and the belt is moving and **contracted**.

Suppose **five** parts of belts are contained in one side of the inner frame.

And each belt on the **upper** side extends a wire in the **horizontal** direction.

As a result, the detector ( which counts the number of wires ) **always** feels **five** wires in Fig.28 left case.

In Fig.28 right, from the viewpoint of the moving belt (= K' ), the belt **returns** to its rest length, and the inner frame is moving and **contracted**.

So only **three** belts are included in one upper side of the frame in K'. ( ← **5 = 3** )

In this case, only **three** horizontal wires are detected by the detector

This is clearly fatal paradox.

Because the number of wires which detector feels **decreases** from 5 to 3 only by observer's movement !

**Continuous** act ( such as Coulomb force and long wires ) is the weak point of special relativity.

*(Fig.28') Each belt with long wire and point detector.*

We supplement Fig.28 with Fig.28'.

Each belt is supposed to have long *wire*, which is always **parallel** to its belt.

As shown in Fig.28', point detector can detect this wire, when its belt exists **Only** on the **upper** side of the frame.

As a result, fatal paradox appears in the detected number of belts on the upper side ( 5 → 3 ).

This detector detects this wire (= belt ) **continuously**, when the belt is on the upper side.

So the logic of different times in defferent inertial frame **cannot** be used here, as shown in simultaneous problem.

**Continuous** act reveals **true** paradox.

See also Special relativity "really" ends.

*(Fig.29) Moving pole and barn *

Here one pole is **moving** and Lorentz-**contracted** with respect to **K** frame.

In K frame, barn is at rest, and the length of barn is the **same** as Lorentz-contracted pole.

So when we pull down the shutter at time "**t**", the pole can **enter** the barn completely.

*(Fig.30) Moving pole and barn *

In K' frame, the moving pole is at rest, and instead, **barn is moving** in the opposite direction.

So in K' frame, barn is Lorentz contracted instead of pole.

As a result, the pole **cannot** enter the barn **only** in K' ?

(= pole - barn paradox. )

*(Fig.31) Clock ticks differently in K and K' frame.*

This is what we call **simultaneous** problems of special relativity.

When the time in **K** frame is "**t**", the times at x=a and x=0 in K' frame are **different**.

So in K' frame, the time **t'** at **x = a** is **earlier** than that of x = 0.

*(Fig.32) From moving pole, the front wall of barn is broken.*

As a result, in K' frame, first, the pole **collides** with the front wall of the barn ( and the wall is broken ).

Next, the pole enters the barn, and then the shutter is down.

So also in K' frame, the pole can enter the barn, they insist.

But this pole-barn paradox **cannot** solve the **basic** problem contained in special relativity.

As a result, **fatal** paradoxes of conveyor belts and Ehrenfest happen.

*(Fig.33) Right-angle lever rotates or not ?*

In Fig.33 left, two forces acting on the lever are in **equilibrium** and the torque is zero with respect to the rest frame observer. So the lever is **not** rotating.

But in Fig.33 right, due to Lorentz contraction of one arm and the change of the force ( see this (p.232), this (p.675) ), this lever **rotates** just by simple observer's movement ! ( See this page. )

This right-angle lever paradox has NOT been solved, and shows special relativity is **wrong**.

( As far as I check various websites, the important transformation of ordinary force ( NOT **artificial** 4-force ) is rarely seen. )

*(Fig.34) Observer's looking power moves the charged particle ??*

This is clearly a paradox, and has **NOT** been solved.

By the simple observer's movement, the external charged particle is attracted to the electric wire (S'), though from the stationary observer (S) they are not attracted to the **neutral** wire.

Charge and currents are **four-vector** current, and transform like spacetime under Lorentz transformation, as shown on this site (p.3).

This direction is the **weak point** of the special relativity. See this page.

Because accordng to the special relativity, new strange charges are **generated** just by simple observer's movement !

*(Fig.35) Electrons teleport to the lower wire → repulsive force ?*

According to the **four-current** of special relstivity, minus charges of the upper wire **teleport** to the lower wire just by simple observer's movement !

In this case, fatal paradox appears as shown in Fig.34.

And as you notice, the state of Fig.35 is very **unnatural**.

Because it is natural that the strong **repulsive** force among electrons in the lower wire does **NOT** allow this teleportation.

As a result, special relativity, which **contradicts** the law of nature, is wrong.

*(Fig.36) 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.

*(Fig.37) K and K' are moving in the opposite directions.*

In Fig.37 left, K' is moving at v in the x direction with respect to K.

But from the viewpoint of moving observer K', K is moving in the minus x direction at v (= Fig.37 right ).

So, we just exchange their coodinates, and replace v by -v in ordinary transformation of

*(Eq.4)*

The coordinate in K' frame is ( t', x', y', z' ), and K frame is ( t, x, y, z ).

Inverse transformation of Eq.4 becomes

*(Eq.5)*

If you substitute Eq.5 into Eq.4, you can confirm Eq.5 is right.

*(Eq.6) Time dilation of a moving clock K'.*

Again, K' frame is moving at v in the x direction with respect to K frame.

Suprisingly, the clock fixed at **x' = 0** of **K'** frame ticks **more slowly** than the observer at rest in K frame ! ( **dt > dt'**, see this site. )

Substituting "x' = 0" into the first equation of Eq.5, you can get Eq.6.

*(Eq.7) Time dilation of a moving clock K. *

From the viewpoint of K' frame, K frame is moving in the opposite direction.

Conversely, the clock fixed at **x = 0** of **K** frame ticks **more slowly** than K' frame. ( **dt < dt'** )

So, **irrespective** of K or K' frames, a **moving** clock ticks more slowly than stationary one.

*(Fig.38) Which clock ticks more slowly ?? *

So according to the special relativity, the clock in the **moving** frame always ticks more slowly.

From K observer, K' is moving ( K' < K ). But from K' observer, K is moving ( K < K' ).

As a result, we **cannot** know which clock ticks more slowly.

This is clearly a paradox ( = twin paradox. ) and is one of mysterious phenomena in the relativistic world.

Ordinary relativity textbooks often say this twin paradox is not a real paradox, and is caused by our misunderstanding about the special relativity.

And they often say we have to use the general relativity to solve this paradox.

In fact, the famous GPS time shows twin paradox, which means GPS has **nothing** to do with relativity.

And transverse Doppler effect includes this twin paradox.

*(Fig.39) Who ordered the muon ?*

It is natural that we think the lifetime of the muon becomes longer 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.

*(Fig.40) Twin paradox in the two identical satellites.*

According to the relativists, GPS satellite is **moving faster** than us, so the GPS clock ticks **slower** than ours by 7 μs per day.

And due to the weaker gravity, GPS clock ticks faster by 45 μs per day. As a result 45-7 = 38 μs faster.

You may notice, this GPS time calculation includes **twin paradox**, as I explained above.

Because from the veiwpoint of the moving satellite, **our observers are moving faster**.

And as shown on this page, when the two identical satellites are moving in the opposite directions on the same orbit around the earth, their clock times clearly show paradox.

We can prove these are clearly twin paradoxes using general relativity including the centrifugal potential.

So famous **GPS** satellite relativistic corrections which uses special relativity include **twin paradox** and are **wrong**.

Atomic clock of the satellite uses **frequency** of the electromagnetic waves.

( We are **NOT** looking at the **hands** of their clocks. )

It is natural that we think some medium in the air causes their frequency difference, rather than **fictional** gravitons.

*(Fig.41) Special relativity ( Dirac equation ) is one of most influential theories.*

In spite of those fatal paradoxes, the relativity survived for more than 100 years.

So we **have to explain the reason** why the relativity with fatal paradoxes survived.

( And we have to think about the reason why the ordinary relativity textbooks **NEVER** write about these important paradoxes. )

The main reason exists in the very important Dirac equation.

Before the computers become popular in 1980s - 1990s, the Bohr-Sommerfeld model could not deal with very compilicated **three-body helium** atoms.

In this situation, Dirac equation could combine spin and relativity properly.

And **unrealistic** quantum mechanics dislikes **real** de Broglie waves (= ether ), and loves strange **parallel-worlds**.

Of course, Dirac equation is just equal to Klein-Gordon equation, in which the relativity has survived.

*(Fig.42) 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.

*(Fig.43) 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.43 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.43 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. )

*(Fig.44) No refraction → telescope needs to be inclined.*

And as shown in Fig.42B and 44, the explanations about aberration using ether drag are often misunderstood.

From the **viewpoint** of the moving earth, the emitted light from the star changes its direction like the rainfall.

In Fig.44, an apparent velocity of the light is a little larger in the outer space, and after it enters the "earth ether", its velocity becomes "c".

In this case, we need to consider the **refraction**.

When we calculate the angle of the aberration, we usually consider sinθ is equal to tanθ

This means we can neglect the **second** order effect of **v/c**. ( "v" is much smaller than "c" ).

So no refraction happens, and we need to **incline** the telescople for the light to reach the bottom of it.

*(Fig.45) If ether "drags" light → no aberration ??*

I found a **wrong** counterargument to ether dragging, as shown in Fig.45.

They insist, the light from some star is dragged by earth ether at the horizontal velocity of "v", the instant it enters earth ether.

As a result, from the viewpoint of the observer moving with the earth, he cannot see aberration like Fig.45 middle, so ether dragging is wrong, they insist.

Of course, this explanation is **wrong**. Can you find the fault of this ?

According to **Snell's** law, the refractive index (= n ) can be expressed as the ratio of velocities in two different media ( = v1/v2 ).

This is equal to the ratio of light angles ( v1/ v2 = sin θ1/ sin θ2 ).

If their objection is right, this ratio becomes **infinity** ( θ2 → 0 ), which is **impossible**.

So the right answer is, the light from the star is **little** bent (= Fig.44 ), and we **can** observe aberration in ether dragging theory naturally.

*(Fig.46) 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.47) Transverse Doppler effect = time dilation !?*

In Fig.46,47, 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.

*(Eq.8) Original light frequency (= ν _{0} ).*

During the time of **dt'**, the number of emitted light (wavelengths) from the source is **dn'**.

So the light frequency in K' frame is **ν _{0} = dn/dt'**.

*(Eq.9) Observed frequency (= ν' ) becomes lower than ν _{0}.*

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.

*(Fig.48) 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.48, 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,

*(Eq.10)*

The frequency is inverse proportion to the wavelength.

So the observed light frequency (= ν') becomes

*(Eq.11) Observed frequency (= ν' ) becomes lower than ν _{0} also in classical picture.*

Eq.11 is equal to Eq.9.

So we can explain transverse Doppler effect by the classical electromagnetic wave.

As you notice, the result of Eq.9 and Eq.11 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 ν_{0}.

*(Fig.49) Relativistic invariance = Math and infinity. *

You may hear the relativity and quantum mechanics are incompatible with each other.

But in fact, the special relativity is the **basis** of all important relativistic theories such as QED, standard model and supersymmetry through Dirac equations.

Relativistic restriction is **too strict**, so all we can use is only very abstract Math, in which there are no concrete objects.

Furthermore, to keep Lorentz symmetry, relativistic wavefunction must include infinite kinds of momentum and energy, which diverge to **infinity**.

Dirac and Pauli **disliked** QED, which **artificially** removes infinity.

Pauli wrote a letter to Dirac. In this letter, he said he wanted to quit a physicist and might be a novelist, because he was dissapointed at the fact **relativistic** quantum field theories **always** diverge to infinity.

*(Fig.50) Positron contradicts basic physical principle.*

Positron is the antiparticle of the electron.

The positron has a opposite charge +e and the same mass as an electron.

According to the current quantum theory, a positron easily **annihilates** with electron, forming γ rays.

The important point is that the existence of these antiparticles are completely **inconsistent** with basic physical principles.

This means antiparticles are **unreal**.

*(Fig.51) Positron is produced from photon. Why "nucleus" is necessary ?*

According to this site and this site, when a high-energy electron comes **near** a nucleus, and is deflected in its path, it **radiates** photons.

These photons spontaneously **turn** into an electron-positron pair.

But if this explanation is right, the nucleus (= target ) is **NOT** necessary.

**ONLY** under the strong electromagnetic field, each electron can radiate high-energy lights !

Then why they must **collide** electrons with other nuclei to produce positron ?

The reason of this is very **unreasonable**.

*(Fig.52) Momentum of incident light suddenly becomes zero ( p = 0 ) !?*

This website says,

----------------------------

If the photon only just had enough energy to create the mass of the electron-positron pair then the electron and positron will be **at rest**.

This could **violate** the conservation of **momentum** since the photon has momentum ( p = E/c ) and the two resulting electrons have **none** ( p = 0 ) if they are stationary ( momentum = mass × velocity ).

This means that the pair production **must** take place **near** the nucleus since they can **absorb** the momentum of the original photon.

-----------------------------

In fact, this explanation is self-**contradictory**. See also this site.

It is **impossible** for the nucleus to absorb **ONLY** momentum, **without** energy.

Because absorbing momentum means absorbing some **kinetic** energy.

*(Fig.53) Only momentum is NOT conserved.*

As shown in Fig.53, when the incident photon has the energy of just **2mc ^{2}**, one pair of electron and positron can be created, according to Einstein relation.

But in this case, these resultant electron-positron do **NOT** have kinetic energy at all.

Because all energies of the photon are used for their **mass** energy.

Of course, the incident light has momentum ( p = E/c ).

But the resultant electron-positron has **NO** momentum ( p = 0 ).
This is strange.

*(Fig.54) Convenient nucleus can absorb "excessive" momentum ?*

Of course, the total momentum ( and energy ) **must** be conserved.

To be consistent with this basic law, they think the nucleus near photon **absorbs** this excessive momentum.

As you may notice, this explanation is **unreasonable**.

*(Fig.55) This nucleus has "momentum", but NOT kinetic energy !?*

Strange to say, this nucleus has momentum, but **NO** kinetic energy !

In the realistic world, this is **impossible**.

This fact clearly shows pair production of positron-electron is impossible.

A positron is just a positive ion or proton ( or **scattered** electrons ), considering it always needs **collision** with nuclei.

As shown on this site (p.17-18) and this site, photon-photon collider just collide **charged** particles and **virtual** photons. So they **don't** use "real" light (= photon ) at all.

*(Fig.56) Photon's ( light ) energy is just converted into a pair.*

In this section, we explain why positron production is **unrealistic**.

In Fig.56, photon's energy is just 2mc^{2}.

So a pair of electron and positron can be created, and they are **at rest**.

K observer is stationary, too.

*(Fig.57) If photon has lower energy, this pair production is inhibited.*

As a result, if the light source emits photon with **slightly lower** energy (= E - ε ) than Fig.56, a pair production does **NOT** happen.

Because the photon energy **cannot** reach 2mc^{2}.

*(Fig.58) When observer moves, new "kinetic energy" is given to position and electron ?*

If the observer of Fig.56 starts to move (= K' frame ), both a positiron and an electron also start to move from the perspective of this K' observer.

So in K' frame, resultant positron and electron have more **kinetic** energies
**in addition to** the original rest mass energies.

Though the light sourse is emitting the **same** photon.

*(Fig.59) When light sourse emit photon with lower energy ... ?*

As shown in Fig.58, if resultant positron ( electron ) has **excessive** kinetic energy, the light sourse can make emitted photon's energy **lower** to produce a pair of positron and electron at rest.

But this fact clearly **disagrees** with Fig.57.

This means a pair production of antiparticle is **inconsistent** with special relativity.

*(Fig.60) *

According to Doppler effect, the phoron (= light ) energy increases in K' frame than K frame.

Because light frequency becomes **higher**.

This means the amount of photon's energy for a pair production **depends** on observer's movement !

This is strange.

*(Fig.61) Kinetic energy depends on observer's motion !?*

If the energy can be converted into rest mass energy of antiparticle, the observer's motion can control this production ?

Because object's velocity (= kinetic energy ) **depends** on oberver's motion.

Even if a positron cannot be produced in K frame, it can be generated in K' frame.

This **paradox** clearly shows the existence of antiparticle is very **doubtful**, as shown on this page.

*(Fig.62) Distance between resultant position and electron is zero ... V = -∞ ?*

When the photon's has the energy of just 2mc^{2}, resultant positron and electron are **at rest**.

But in this case, the distance between them is almost **zero**, which means potential energy between them is **minus infinity** !

So the energy is NOT conserved ( 2mc^{2} → 2mc^{2} - ∞ ).

This is also a **paradox**.

*(Fig.63) Even when we break mass into pieces, total mass remains the same.*

The important point is that the concept of mass energy is **unreal**.

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**.

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**.

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.12)*

In Eq.12, "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.12, the proper time is

*(Eq.13)*

Eq.13 is Lorentz invariant scalar ( see Fig.64 ).

*(Fig.64) *

We can treat this proper time as a "**constant**" under Lorentz transformation.

*(Eq.14)*

Considerting Fig.64 and Lorentz transformation, the special relativity defines **four vector** as

*(Eq.14')*

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.15)*

Eq.15 can be expressed as

*(Eq.16)*

From Eq.12-Eq.14 (= proper time), the denominator of Eq.16 can be considered as a constant.

So Eq.16 changes as **x compoment** of the four-vector under Lorentz transformation.

Replacing x by **ct** (= zero component of the four-vector, see Eq.14' ), Eq.16 becomes

*(Eq.17)*

From Eq.17, we can define the **zero component** of the four vector, as follows,

*(Eq.18)*

where E is the relativistic energy of

*(Eq.19)*

Here we use the notation, p_{0} = - p^{0}.

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.20)*

As you see in Fig.64, and from Eq.15 and Eq.18, these relativistic momentum and energy satisfy the following **important** equation,

*(Eq.21)*

The important point is that Eq.21 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.22)*

Using Eq.22, Eq.21 can be expressed as

*(Eq.23)*

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.24)*

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**.

See also this calculation.

In this section, we calculate constant light speed "c" under Lonretz transformation.

**K'** frame is **moving** at velocity "v" to the right along x axis relative to K frame.

*(Ap.1) K' frame is moving to the right relative to K.*

At time **t = 0**, the light is **emitted** from the source at the origin.

( At time t = 0, both origines in K and K' frames are in the **same** position. )

*(Ap.2) Light speed is constant "c", in both K and K' frames.*

After some time ( t in K frame, t' in K' frame ), 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 observers, according to **strange** special relativity.

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

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

To do so, the variables of **time** and space must transform like,

*(Ap.4) Lorentz transformation.*

According to Lorentz transformation of Ap.4, the moving clock **ticks slower** than one at rest !

And the **length** of any object in a moving frame appear contracted. See also this site.

This **unnatural** transformation causes serious paradoxes.

*(Ap.5) Classical vs. Lorentz transformation. *

As shown in Ap.5 upper equations, **only** x coordinate transforms like x' = x - vt, when K' observer is moving in the positive x direction, in **classical** mechanics.

In this case, two equations of Ap.3 **cannot** hold.

*(Ap.6) Classical transformation.*

But of course, in this classical mechanics, fatal paradoxes do **NOT** appear.

*(Ap.7) Lorentz transformation is unrealistic.*

When you substitute Ap.4 into the first equation of Ap.3, you find the second equation of Ap.3 also holds true.

This is called "**Lorentz transformation**".

But as you feel, it is very **unrealistic** to think the clock **ticks slower** only by object's motion.

The concept of "time" should be **common** irrespective of object's velocity.

*(Ap.8) Michelson-Morley experiment = "ether" moving with the earth ? *

When you look around us, **all** objects including air are moving with the earth.

All these things consist of electrons and nuclei which attract each other by **electric** field.

So if we assume the **ether** moving with the earth, we can **naturally** explain constant light speed "c", **without** depending on strange Lorentz transformation.

*(Ap.9) Velocities change from different frames. *

K' frame is moving in the x direction at "v" with respect to K frame.

From the observers of K and K' frames, the **velocity** of the **same one particle** can be expressed as

*(Ap.10)*

where u(t) is the velocity from K, and u'(t') is that from K'.

As shown in Ap.10, the velocity of the same one particle looks *different* in different frames.

Because the time and space change in different ways in different frames.

This velocity u(t) is *different from v of β* in Lorentz transformation (Ap.11).

*(Ap.11)*

"v" of β means the velocity of K' **frame itself** ( not particle ), which is constant in the special relativity.

The particle's coordinate ( x, y, z ) is the **functions** of the time t (or t' ), because its position is changing with time t.

So the particle's position ( x, y, z ) is NOT independent from the time t.

For example, the time transformation of Ap.11 can be expressed as

*(Ap.12)*

According to AP.11 (and Ap.12), the velocity in the **x** direction **u' _{x}(t')** from K' can be replaced as

As I said above, inverse Lorentz tansformation is

*(Ap.14)*

From Ap.14, we have

*(Ap.15)*

Substituting Ap.15 into Ap.13,

*(Ap.16)*

Solving Ap.16, we obtain

*(Ap.17)*

Using Ap.11 and Ap.15, the *y* component of velocity becomes

*(Ap.18)*

Substituting Ap.17 into Ap.18 and solving it, we obtain

*(Ap.19)*

In the same way, the solution of **z velocity** is

*(Ap.20)*

Next we differentiate Ap.17 with respect to t.

*(Ap.21)*

From Ap.11, we get

*(Ap.22)*

Dividing Ap.21 by Ap.22,

*(Ap.23)*

Ap.23 means the **acceleration from the viewpoint of K'** inertial frame.

Here we choose the moment when the particle's velocity u_{x} is just equal to "v" of K' frame's velocity.

So the particle is moving in K frame. But it is at **rest** in K' frame.

*(Ap.24)*

In K', the particle is **at rest**, so it must satisfy Newtonian mechanics using **Newtonian force F'**, as follows,

*(Ap.25)*

Newtonian mechanics of Ap.25 is the basis of the relativistic momentum.

Substituting Ap.24 into Ap.23, we get

*(Ap.26)*

Here we use the relation of

*(Ap.27)*

From Ap.25-Ap.27, we get the **relativistic momentum** ( = p_{x} ).

*(Ap.28)*

To get the relativistic momentum, we have to define as follows,

*(Ap.29)*

The definition of Ap.29 (= transformation of Newtonian force ) is very important.

( x component of Newtonian force does NOT change under Lorentz transformation. )

But this definition is "**artificial**" to get the relativistic momentum.

We suppose the Newtonian force F_{x} doesn't change under Lorentz transformation in Ap.28.

But in other directions, we need to **change** the forces to define the proper relativistic mass.

( So the relativistic momentum is not a "natural" result gotten from the special relativity. )

In K' inertial frame, the acceleration in y direction is

*(Ap.30)*

Differentiating Ap.19 with respect to t,

*(Ap.31)*

Inserting Ap.31 and Ap.22 into Ap.30,

*(Ap.32)*

In Ap.32 we suppose only F_{y} exists.

And u_{y} is zero here .

The particle is moving in the x direction in K frame, and the force F_{y} tries to accelerate the particle in the y direction.

K' is moving in the x direction at the velocity u_{x}. Substituting Ap.24 into Ap.32,

*(Ap.33)*

Using the definition of relativistic momentum of Ap.28 and Ap.33,

*(Ap.34)*

As the particle is at rest in K' frame, we can use the usual classical relation of ( F' = m_{0}a' ) in K' frame.

To match Ap.34 with Ap.28 (= relativistic momentum ), we have to change the force F_{y}, as follows,

*(Ap.35)*

This definition is inconsistent with Ap.29.

*(Ap.36) Summary in Newtonian forces and relativistic mass.*

The important point is that these artificial definitions cause **fatal** "right-angle lever paradox (Trouton-Noble experiment paradox)".

*(Ap.37) Right-angle lever paradox.*

Here is a right angle lever with a stationary point and two arms.

This lever is moving with K' frame, and is in equilibrium in K' frame.

( In K' frame, two arm's length and forces are equal, so its torque is zero. )

*(Ap.38) Rotate only in K frame ?*

But in K frame, the lever is moving in the x direction, so
one of the lever's arms is Lorentz contracted, and only F_{y} is weakened.

So the torque is NOT zero only in K frame, and the lever rotates **only** in K frame just by simple observer's movement !

*(Ap.39) Which is true ?*

As shown on this page, this fatal paradox has not been solved, and shows relativistic theories such as QED, standard model and string theory are all wrong.

Because all these theories depend on the relativistic momentum and energy through Dirac equation.

Next we try another method to get the relativistic momentum and energy.

We define " **four-vector velocity** " (= **ω** ) , as follows,

*(Eq.51)*

where the proper time (= τ ) is Lorentz invariant, so Eq.51 change as **four-vector** such as (t, x, y, z) under Lorentz transformation.

From here, we use the next notation of

*(Eq.52)*

**i = 1, 2, 3 components** of four-vectors are

*(Eq.53)*

where Eq.12 is used.

And **ω ^{0}** becomes

where we use

where g (or η ) means Minkowski metric tensor of

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

*(Eq.56)*

where Loretnz matrix is

*(Eq.57)*

Eq.56 means

*(Eq.58)*

As a result,

*(Eq.59)*

So we can get the relation of

*(Eq.60)*

Here we define new equations of

*(Eq.61)*

Using Eq.53 and Eq.54, we can get

*(Eq.62)*

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

We differentiate Eq.62 by the proper time ( τ ), and divide it by 2,

*(Eq.63)*

where Eq.61 is used.

We introduce the new variable ω_{μ}(τ) and f_{μ}(τ) irrespective of reference frame.

So the next relation is naturally satisfied.

*(Eq.64)*

As shown in Eq.51, ω_{μ}(τ) change as *four-vector*. So if **f _{μ}(τ) also change as four-vector**,

We can get Eq.64.

So f_{μ}(τ) of Eq.61 also change as four-vector like ω_{μ}(τ).

We call these f_{μ}(τ) " **four-vector force** ".

Here we define **f ^{i} (τ)** (i = 1, 2, 3 ) as

where F means Newtonian force.

This definition of Eq.66 is "

And substituting Eq.53, Eq.54 and Eq.66 into Eq.64,

*(Eq.67)*

From Eq.67, the solution of 0 component ( = **f ^{0} (τ)** ) becomes

Using Eq.12, Eq.61 can be expressed as

*(Eq.69)*

Substituting Eq.53 and Eq.66 into Eq.69, we can get the equation of motion of

*(Eq.70)*

So we get the **relativistic momentum ( = p )**, as follows,

*(Eq.71)*

And substituting Eq.54 and Eq.68 into Eq.61,

*(Eq.72)*

So we get the **relativistic energy ( = E )**, as follows,

*(Eq.73)*

These results are the same as the upper section.

As I said, the definition of Eq.66, 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.

According to Maxwell's equation, the **current density** (= **J** ) and **charge density** (= **ρ _{e}** ) satisfy

Of cource, the total charge is *conserved* irrespective of reference frame,

So the equations of Eq.74 must be Lorentz-invariant.

( See this page. )

But this definition of Eq.74 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.74 can be expressed using four vector ( x^{μ} ), as follows,

*(Eq.75)*

*ct* can be replaced by x^{0}

And if we define the new four vector (= **four current density** ), as follows,

*(Eq.76)*

Eq.75 can be expressed as

*(Eq.77)*

Using Lorentz transfomation of Eq.56, the differentiation by x^{μ} is

*(Eq.78)*

Substituting Eq.78 into Eq.77, we have

*(Eq.79)*

As a retult, Eq.77 (= Eq.74 ) proves to be **Lorentz invariant**.

2014/5/16 updated. Feel free to link to this site.