Top page (correct Bohr model. )

Strange "spin" is NOT a real thing

True paradoxes of Special relativity.

*(Fig.1) Right angle plate is bent by observer's movement ? ← Paradox !*

In Fig.1, the right angle plate (= brown ) is moving in the upper direction at constant velocity along the rest post standing upright.

These plate and post are **rigid** bodies, so they **cannot** be bent just by observer's movement.

An observer is at rest in S frame relative to the post.

In S' frame, the observer is moving to the right with respect to S frame.

Surprisingly, only in S' frame, this right-angle plate becomes **bent**, though it is **rigid** body.

This is clearly a **paradox** of special relativity.

*(Fig.2) Lorentz transformation.*

As shown on this page and this site, the time and space coordinates transform like Fig.2 by an observer's motion in special relativity.

The time (= t' ) in S' frame changes depending on **both** of the time (= t ) and x-coordinate (= x ) in S frame.

This strange definition of relativity causes fatal **paradoxes**, as I explain on this page.

*(Fig.3) The same time events in S frame occur at different times in S'.*

Substituting the time **t = 0** and each x-coordinate of S frame into the equation of Fig.2, we can know the times at different x-coordinates are **different** in S' frame !

As shown in Fig.3, the time (= t' ) at x = 1 is **earlier** than that at x = 0, though their times are the same ( t = 0 ) in S frame.

This **strange** world is special relativity.

*(Fig.4) The "rigid" plate is bent only in S' frame ! ← Paradox.*

Fig.4 shows how this rigid plate looks from the viewpoint of the observer at **t' = 0** in **S'** frame.

As I said above, the state of Fig.3 is a collection of events at **different** times in S'.

So we need to make their times the **same** ( for example, t' = 0 ).

As more time passes, this plate moves **upward**.

As a result, in S' frame, this right angle plate is **bent**, which means it is **NOT** right-angle.

Considering this plate is **rigid**-body, this "bent" state is clearly a **paradox**.

*(Fig.5) "V-shaped" ( NOT right-angle ) panel fits this plate ?*

Here is "V-shaped" ( rigid ) panel, which just **fits** this bent plate.

At the time of t'=0, this V-shaped panel can be put onto the **bent** plate.

Of course, this "V-shaped" panel means **NOT** right-angle.

*(Fig.6) But this V-shaped panel does NOT fit the right-angle plate in S frame.*

How does the state of Fig.5 look in S frame ?

In S frame, first, only the *left* side of this V-shaped panel is put on the right-angle plate, as shown in Fig,6 left.

After a while ( t > 0 ), the *right* side of this panel is put on this plate.

But this panel and plate are **rigid** bodies, so they do **NOT** fit each other **only** in S frame !

As shown in Fig.6 lower-right, for this panel to completely touch the right angle plate, this plate must **break**.

Of course, it's **impossible**.

*(Fig.7) "V-shaped" does NOT become right-angle in either inertial frame.*

Of course, if this panel is V-shaped in one frame, it does **NOT** become right-angle in other frames.

So the fatal **paradox** appears with respect to **simultaneity** in special relativity.

*(Fig.8) Box + long wire is moving along conveyor belt.*

Here we explain fatal paradox in conveyor belt.

In Fig.8, the metallic inner frame is at rest.

Around this metallic frame, conveyor belt is *moving* counterclockwise, loaded with boxes (= green ).

Each box has long **rigid** wire (= blue ) in horizontal direction.

At the upper left of this machine, there is a **detector** (= red ), which can **count** the wires, which is **penetrating** the detector

*(Fig.9) The relation between detector and horizontal long wire attached to box.*

Each wire is supposed to **always** point in **horizontal** direction.

As shown in Fig.9, **Only** when each box is moving along the **upper** side of this machine, the detector can detect the wire penetrating it.

*(Fig.10) K frame is at rest with respet to this machine.*

The observer in K inertial frame is **at rest** relative to this machine.

In K frame, conveyor belt is moving at velocity "v" along the inner frame, counterclockwise.

Each side of this machine **always** contains **five** boxes.

So the detected wires are always "**5**" in **K** frame.

*(Fig.11) Seen from moving observer (= K' ), detected wires become "3" !? ← Paradox !*

The observer in K' frame is moving to the left at the velocity "v", relative to this machine.

In this K' frame, the detected wires **decrease** from "5" to "**3**" !

This is clearly a fatal paradox of special relativity.

Because just by simple observer's movement, the detected number **changes** from "5" into "3".

*(Fig.12) Each length changes differently in K and K' frames.*

According to Lorentz contraction, moving objects look **contracted** in the moving direction.

In **K** frame, the belt loaded with boxes are moving, so each box ( and belt ) is **contracted** ( < b_{0} ) horizontally.

On the ohter hand, in **K'** frame, inner machine is **moving** to the right, and belt with **boxes** ( on the upper side ) are at **rest**.

So, in K', the length of each belt with box **returns** to its original rest length (= b_{0} ).

And the inner metallic frame becomes contracted ( < l_{0} ) in K' frame.

As a result, the contracted upper side of this machine contains Only "**3**" boxes in K', though it contains "**5**" in K.

*(Fig.13) Lorentz transformation in K and K' inertial frames.*

K' frame is moving at v to the left relative to K frame.

So Lorentz transformation between K and K' frames become like Fig.13.

( **t, x, y, z** ) are time and space coordinates in **K** frame, and ( **t', x', y', z'** ) are in **K'** frame.

Change "v" into "-v" in Lorentz transformation of Fig.2.

*(Fig.14) "5" boxes in K, "3" boxes in K' ← Paradox !*

Here we actually calculate each time and position using Lorentz transformation of Fig.13.

In Fig.14 left, the x coordinates ( x = 0, 3, 5 ) at the time of t = 0 are shown.

As I said in Fig.3, the state of Fig.14 left shows the **collective** states at **different** times in K' frame.

So we need to choose one **same** time ( for example, t' = 0 ) of K' frame to express the state of K' frame.

*(Fig.15) Calculating each time and space in K' frame.*

Substituting each x-coordinate of **x = 0, 3, 5** and **t = 0** into Lorentz transformation of Fig.13, we can know the **corresponding** time and space in K' frame.

As shown in Fig.15 and Fig.16, the time (= t' ) on the left side ( x = 0 ) is **earlier** than that on the right side ( x = 5 ).

*(Fig.16) t' at x = 0 is earlier than t' at x = 5 !?*

So the state of Fig.14 left in K is **collective** states at **different** times of K' frame.

We need to make each time t' the **same** ( for example, t' = 0 ) to know how it **looks** from K' observer.

*(Fig.17) If we look at the conveyor belt at t' = 0 in K' frame ...*

As I said in Fig.12, inner metallic frame is Lorentz contracted ( < l_{0} ), and each belt returns to its original length (= b_{0} ) in K' frame.

So Only "**3**" boxes can be put on the contracted upper side of this machine.

At t' > 0, the "4" and "5" boxes exist on the upper side, as shown in Fig.17.

So at the **earlier** time ( t' = 0 ), these two extra boxes exist on the **right** side along vertical inner frame.

*(Fig.18) Rigid wires are bent Only in K' frame !?*

If special relativity is right, we have to accept **impossible** situation like Fig.18 right.

As I said in Fig.16, the times in K' are different at different x coordinates.

If we try to reconstruct the state at the same time ( t' = 0 ) of all wires and boxes, this long wire becomes **bent** complexly.

The **left** part of this long wire (= 4 or 5 ) is **straight** along the **horizontal** direction.

But the **right** part of the same wire must be **bent** complexly, as shown in Fig.18 right.

*(Fig.19) Rigid wire can be bent in "convenient" way to avoid paradox in detected number ?*

If this **rigid** long wire can be **bent** obeying the time t' of special relativity, this system can **avoid** the paradox of different detected numbers ( 5 ← 3 ).

But of course, this is **impossible**, because the wire and box are **rigid** bodies, which **must** keep the same form.

This bent form of wire is very **unnatural** and **unreal**.

*(Fig.20) Rigid long wire can be bent conveniently ? Or special relativity is wrong.*

If special relativity is correct, the **left** part of this wire is **straight** horizontally.

And **only** **middle** part of this same wire must be **bent** complexly.

All parts contained in the same wire are the same kind of thing with respect to direction and motion.

So this **weird** situation of rigid wire, in which only **one part** is bent, is **impossible**. It means special relativity is **wrong**.

*(F-1) Motion of the box 4 with wire in K frame.*

Here we explain about **unreasonable** phenomenon caused by special relativity.

In F-1, K frame observer is watching the movement of box 4 and its wire.

*(F-2) Rigid wire is "bent" just by simple observer's movement !?*

As I said in Fig.19, this **rigid** wire is **bent** from the viewpoint of K' observer.

Of course, this **cannot** happen in this **real** world, so special relativity contains fatal **flaws** in it.

In events happening at the **same** time in **K'** frame, the place on the left side shows the **future** event in K frame.

And the right side shows the **past** (= earlier ) event.

*(F-3) We can change "future" state of the wire whithout touching it !? ← Paradox !*

Surprisingly, if Nature obeys special relativity, we can change **future** state of the wire **without** touching it !.

In F-3, we suddenly **insert** new path, which will carry the box **upward** ( NOT toward detector ) in the future.

This box has **NOT** arrived at this new path, so it **doesn't** know this existence at all.

In spite of this, the **left** side of wire becomes **straight** toward upper-left, just after inserting this path !

Because, if we insert this new path, this box is going upward **without** turining left in the **future**.

This means we can change the left side (= future state in K ) of this wire without thouching it !

So this relativistic world is completely **unrealistic** and false, considering various fatal paradoxes.

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*(F-4) Small forces at different points at the same time. → long object moves simultaneously.*

Basically, the *transmission* speed of forces must **obey** light speed c ( "superluminal" is impossible ).

So when you accelerate a long object at the **same** time, you need to apply forces to the **different** points **simultaneously**, as shown in F-4.

If you apply the force only to one point of this object, it takes some time (= its total length / c ) to **start** to accelerate it.

As the number of points where force is applied increases, it takes **less** time to start to accelerate it.

In this case, the form and length of this rigid-body do **NOT** change in any places.

So this **can** happen under the **rule** of rigid-object.

*(F-5) If a rigid path is inserted, the whole wire goes upward neglecting small other forces.*

In rigid body, **any** pieces of a long wire **stick tightly** to the nighboring ones through strong **local** potential energies.

So we **cannot** stretch or break **any** single point inside a rigid body.

When we suddenly insert a new path like F-3 and F-5, this rigid wire **cannot** accelerate to the left

So only **one** strong obstacle ( like this path ) **determines** the moving direction (= **upward** instead of left ) of this wire.

Because if **only** the left part of this wire moves to the left, some places of this long wire are **stretched**, which **needs** extremely strong forces ( from both sides ) overcoming **local** potential energy.

To accelerate a rigid body in some other directions, we have to remove **any** single resistance.

If a strong resistance is left, all other small forces become **meaningless**.

As a result, if special relativity is correct, we have to accept **paradoxical** phenomenon in which the **future** state can be **changed** without touching it like F-3. So relativistic world is **false**.

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*(Fig.21) Charge and current paradox is the same pattern.*

On this page and this page, we show special relativity **breaks down** in electromagnetism.

This paradox in electromegnetic fields is the **same** pattern as this moving conveyor belts with long wires.

We consider **moving** boxes as electric current of **negative** charges.

And the **same** amount of positive charges at **rest** are included on each side of the frame.

*(Fig.22) Negative charges decreases from "5" to "3" ← Paradox.*

As shown on this page, using Lorentz transformation of charge density (= ρ ) and current (= J ), we can know the electric current on the upper side changes into **positive** in K' frame from neutral in K.

Current loop contains **two** directions (= horizontal and vertical ).

Relativistic electromagnetism can **NOT** control two different directions.

In Fig.22 left, an external negative charge is at rest in K frame, but this charge is **attracted** toward current in K', because neutral currents in K changes to positive in K'.

This is clearly a **fatal** paradox, and proves special relativity is **wrong**.

*(Fig.23) Special relativity is false → general relativity is false. Why fantasy theories must be believed ?*

General relativity **contains** inertial frame of special relativity as a part of it.

So if special relativity is **false**, general relativity is **false**, too.

As a result, Inflation, black hole and SUSY are all **false**, because they are all **based** on relativity.

In fact, even if we **continue** studying about these **fictitious** concepts such as early universe and black hole, our science does **NOT** make progress at all, which means they are **wasting** much time in these **fantasy** theories.

These concepts including SUSY and string theory (= **10** dimensions ) cannot be confirmed directly, and **useless**, forever.

So it is just **equal** to saying these theories are **unreal**.

*(Fig.24) Two equal forces F _{y} are in equilibrium.*

On this page, we show Lorentz transformation of Newtonian force causes **serious** paradox.

The upper paradoxes such as electromagnetism and conveyor belt are based **directly** on Lorentz transformation itself.

On the other hand, this paradox in force transformation is based on the **new** introduction of relativistic momentum and energy.

So this is **independent** from the upper cases.

In Fig.24, two equal forces F_{y} are applied to the **stationary** lever in K frame (= observer at rest ).

This lever has two equal arms on both sides of a fulcrum, so it is in **balance**, NOT rotate in K frame.

One of these forces (= Fig.24 left ) is **at rest**, and another force ( source ) is **moving** at velocity "v" in x direction.

*(Fig.25) Lever rotates from the viewpoint of moving observer (= K' ) ? *

When the observer is moving at "v" in x direction (= K' ), this lever and left force start to **move** in the opposite direction.

As a result, this force (= Fig.25 left ) is **reduced**, accodring to special relativity

On the other hand, right force looks **stationary** in K' frame, it is **increased** by observer's movement.

As a result, this lever **rotates** clockwise only in K' frame !

This unreasonable transformation of force F_{y} is one of causes of right angle lever paradox.

Of course, this paradox has **NO** solutions, which means relativistic momentum and energy are **wrong**.

*(Fig.26) Twin paradox in the two identical satellites.*

As shown in Lorentz transformation, each time and space coordinate in one inertial frame **corresponds** to that of another frame, **independently**.

So, we **cannot** prove twin paradox within special relativity.

But the "time dilation" experiments using atomic clock ( in moving objects ) are very doubtful due to twin paradox.

To prove twin paradox by going back to the **same** place, we **have** to depend on general relativity.

Because general relativity adopts a **different** kind of concept such as **central** gravitational force.

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.

Seen from one satallite (= A ), the clock of another satellite (= B ) ticks **slower**.

But seen from "B" satellite, the clock of "A" satellite ticks **slower**. So which clock is slower ?

General relativity can make these two satellites **meet** each other, using gravity.

So twin *paradox* is **revealed** with the **help** of general relativity.

*(Fig.27) Negative charge is attracted toward wire ONLY in S' frame ?*

On this page, we show charge densities included in the upper ( or lower ) wire changes by oberver's movement.

In this section, we review the transformation of charge and electric field in different inertial frames.

*(Eq.1) The universal relation between charge (= ρ ) and current (= J ).*

As shown on this page, the increase in charge density (= ρ ) **must** be equal to the gradient of current density (= J ) in all reference frames.

Because it is **impossible** that "charges" suddenly **disappear** somewhere.

*(Eq.2) Lorentz transformation of charge (= ρ ) and current (= J ).*

To satisfy the relation of Eq.1, the charge density (= ρ ) and current density (= J ) **must** transform like Eq.2 under Lorentz transformation.

Apostrophe' denotes S' frame, which is moving in x direction at v, relative to S frame.

*(Fig.28) Total charge Q = Q' in S and S' frames.*

Using Lorentz transformation of Eq.2, we can know the total charge Q is always **conserved** in different inertial frames.

In Fig.28 left, a cube of charge density (= ρ ) is at rest in S frame.

The length, width, heigh of this cube is supposed to be x, y, z.

*(Fig.29) *

Seen from S' observer moving in x direction at v,
only the length of moving direction (= x' ) is Lorentz-contracted.

And using Eq.2, charge density (= ρ' ) is **increased**, as shown in Fig.29.

*(Fig.30) Total charge Q does NOT change. *

Total charge Q is given by the charge density (= ρ ) × the volume (= xyz ) of this cube.

From Fig.29, you can understand the total charge Q does NOT change in S' frame ( Q = Q' ).

This means the total charge "e" of an electron and a proton is the **constant** value, independent from observer's motion.

*(Fig.31) Gauss law and transformation of electric field E _{x}.*

When some charge is enclosed by the surface S,
this total charge is given by the surface integral of electric field over S.

According to special relativity, the electric field E and Newtonian force F in the moving direction ( in this case, E_{x} ) do **NOT** change under Lorentz transformation.

In Fig.31, there is no contradiction between the electric and Newtonian force acting on an external charge (= + ).

Because they are the same in different frames.

From Fig.30 and Fig.31, we can know Gauss law, which defines the relation of electric field and charge, is always **effective** even when the charge is moving.

*(Eq.3) Lorentz transformation of electromagnetic fields.*

As shown on this site and this site (p.91), Lorentz transformation of E, B fields become like Eq.3.

This transformation is indispensable to unite special relativity and Maxwell equation.

*(Fig.32) Lorentz transformation.*

Using Lorentz transformation of Fig.32, we can prove Gauss law is **effective** also in y and z directions.

As shown in Fig.33, the charge density (= ρ ) in x-y plane is increased in S' frame.

*(Fig.33) Gauss law is always valid in S and S' frames.*

In **proportion** to this increase in charge density, the electric field E_{z} ( or E_{y} ) is increased, too.

As a result, the surface integral of electric field becomes equal to enclosed total charge in any reference frames (= Gauss law ).

*(Fig.34) Surface intagrals over different areas give the same charge Q.*

Of course, if the amount of total charge is the same, any **different** surface integrals of electric field around the charge must give the **same** amount of charge.

If the strengths of E_{x} and E_{y} change differently under the same total charge, these surface integrals give **different** values, which means wrong.

( In this case, the surface integrals of Fig.34 left and right over **different** forms of cubes give **different** Q. )

*(Fig.35) *

So, if the total charge included is the **same**, the strengths of electric field in all directions do **NOT** change under Lorentz transformation.

And fatal paradox of relativistic electromagnetism appears, as shown in Fig.27 and Fig.36.

*(Fig.36) Electric field E' _{x} is zero, but E'_{z} is NOT zero. ← Paradox ! strange charges.*

*(Fig.37) Observer on the earth (= A ) and one moving with muon (= B ).*

Though it is said that the time dilation can be **confirmed** (← ? ) by muon's *longer* lifetime, this time dilation is self-**contradictory**. See also this and this.

In Fig.37, from the perspective of an observer on the *earth* (= A ), the muon is **moving**, so *muon*'s clock is time-**dilated**. See this site.

Suppose muon's lifetime is "**4**" seconds, while **4** seconds have elapsed in muon's frame, **8** seconds have elapsed on the earth.

So in the above case, the **muon**'s clock is time-**dilated**, and its *lifetime* looks **longer** (= Fig.37 left ).

But from the perspective of the *observer moving* with muon (= B ), the clock on the **earth** is time-dilated.

Because, the earth is **moving** and the muon is *at rest* in muon's frame (= Fig.37 right ).

As a result, while **4** seconds elapse in muon's frame, only **2** seconds elapse on the earth. (= Muon's lifetime is **shorter** ! )

This is clearly a twin paradox, and shows the experimental facts of "time-dilation" is *doubtful*, and **wrong**.

The same thing can be said about the GPS time dilation (← **far-fetched** interpretation ).

*(Fig.38) Light source is moving at "v", and emitting light with frequency f'.*

It is said that time dilation was confirmed using **airplanes**, these experiments depended on many artificial corrections. Basically when a plane comes back to the **original** place, it causes **twin** paradox.

In these sites ( this and this ), they argue that atomic clocks using emitted light's **frequency** confirmed time dilation in moving objects. But due to **twin** paradox, the time dilation becomes **opposite**, which means these confirmations are **doubtful**.

In Fig.38, the light source is moving to the right at a velocity of "**v**", and emitting light with a frequency of **f'**.
Time period between wave crests in the source rest frame is (= **Δ t'** ).

Here the source's time is t' and the observer's time is t.

*(Fig.39) Clock in moving source is time-dilated ?*

According to special relativity, the **moving** clock runs more **slowly** than that at rest.

So, while **Δ t'** elapse in the source's clock, **more** time (= Δ t > Δ t' ) elapse in the observer's clock.

*(Fig.40) Observed light frequency decreases ? *

As a result, they argue that the observed light frequency decreases (= **f < f'** ). This is called "redshift"

Because of the time dilation, **more** time elapse in rest frame during one light wavelength ( **Δ t > Δ t'** ).

*(Fig.41) Source is at rest, and the observer is moving *

But from the perspective of light source (= **rest** frame of source ), the **observer** is **moving** in the opposite direction.

*(Fig.42) Observer's clock ticks more slowly in this case ?*

As a result, the **observer**'s clock ticks more **slowly** than the source's clock in this frame.

Because the observer is moving, and the source is at rest.

*(Fig.43) Observed light frequency (= f ) "increases" in the source's rest frame ?*

Due to time dilation in observer's clock, the observed light frequency **increases** (= blueshift ) in this case.

This is clearly **inconsistent** with "redshift" in Fig.40.

*(Fig.44) Which is true ? Redshift or blueshift ?*

As you see, we don't know which will happen, redshift or blueshift.

This is clearly **paradox**, and shows time dilation using atomic clock (= GPS, transverse Doppler ) is very **doubtful** and wrong.

In fact, the right answer is "*blueshift*", **different** from the current standard's claim, if special relativity is right.
Because when the light source is moving, the light is emitted "**twisted**", causing *blueshift*.

Redshift is caused by the "medium-Doppler shift" (= classical ), as is explained on this page.

So the interpretation in GPS and transverse Doppler by atomic clocks **contradicts** relativity.

2015/1/6 updated. Feel free to link to this site.