*(Fig.1) Force F _{y} acting on a stationary mass (= m_{0} ) seen by a stationary K observer appears to decrease to F'_{y} seen by a moving observer K'. *

In the upper figure, a stationary object with rest mass m_{0} is pulled by force F_{y} as seen by a stationary observer K.

According to Einstein relativistic theory, as seen by an observer K' moving rightward at a velocity of v, this object appears to move leftward, and the force F_{y} (= or F_{⊥} ) acting on this object magically appears to **decrease** to F_{y}' = F_{y}/γ where γ is Lorentz factor γ = 1/square root of 1-v^{2}/c^{2}, which means "**moving** force F_{y}'" decreases or **weakens** ( this p.15, this-last, this p.35, this p.5-(44), this p.25, p.45-(7.14) ).

This unphysical force change seen by differently-moving observers K and K' is necessary to satisfy the ad-hoc relativistic mass, energy and momentum p relation where force F is equal to the time derivative of relativistic momentum p (= F = dp/dt ).

On the other hand, the mass m_{0} seen by a stationary K appears to increase to m = γm_{0} called relativistic mass as seen by K' according to Einstein relativistic theory.

This unphysical force change F_{y} → F'_{y} seen by different observers causes serious **irreparable** paradoxes showing Einstein relativity and relativistic mass energy are **false**.

*(Fig.1') Electric force F _{y} acting on stationary plates with positive and negative charges attracting each other seen by a stationary observer K also appears to decrease to F_{y}' as seen by a moving observer K' in relativity.*

Einstein relativistic theory demands that force F_{y} changes as seen by differently-moving observers K and K' to satisfy relativistic energy, mass and momentum relation.

Also in (paradoxical) relativistic electromagnetism, we can know that the electromagnetic **force changes** depending on different observers in the same way as Fig.1 ( this p.35-36 )

In the upper figure, two stationary plates which are positively and negatively charged (= ±q ) are attracting each other by the electric force qE_{y} as seen by the stationary observer K.

When seen by the K' moving at a velocity v in x direction, these two plates appear to be moving in -x direction at v, which motion causes fictitious magnetic repulsion between these two plates, and **decreases** the force F_{y} to F_{y}' = F_{y}/γ in the same way as Fig.1

The electric attraction (= qE_{y}' ) seen by K' increases ( E_{y}' = γE_{y} > E_{y}, this p.14 ), but new magnetic repulsion (= qvB_{z}' = Lorentz magnetic force where B_{z}' = -γv/c^{2}E_{y}, this p.10 ) is stronger and eventually decreasing the total force (= electromagnetic attraction between two charged plates ) from F_{y} to F_{y}' according to Einstein relativity.

*(Fig.2) A stationary rectangular rail pulled by two equal forces (= upper force F _{y} is at rest, lower force F_{y} is moving in x direction ) seen by a stationary K appears to move downward seen by a moving K', which is paradox ! *

In the upper figure, a stationary rectangular rail is pulled by the upper force F_{y} at rest and the opposite equal lower force F_{y} moving in x direction as seen by a stationary observer K. ← upper force F_{y} = lower force F_{y}, so the rail remains at rest by these two balanced opposite forces seen by K

But as seen by another observer K' moving in x direction, the upper force F_{y} appears to be moving in -x direction and **decrease** (= F_{y}/γ ) due to relativistic force transformation.

And as seen by the K' observer moving in x direction, the lower force F_{y} appears to be at rest, hence increase to γF_{y} from F_{y} seen by the stationary K.

As a result, the original **stationary** rail (= due to two balanced equal upper and lower forces ) seen by the stationary K appears to **move downward** (= due to two unbalanced unequal upper and down forces ) seen by the moving observer K'.

This is clearly **paradox**, and Einstein relativistic theory is **false**.

Right angle lever (= Trouton-Noble ) paradox is also one of fatal unsolvable relativistic paradoxes based on this unphysical force transformation.

*(Fig.3) Einstein relativistic energy (= E ) and momentum (= p ) contain only "definite constant values" about a photon (= light ) such as a photon's zero constant rest mass (= m _{0} = 0 ) and a photon's velocity (= v ) equal to the constant light speed = c, which cannot explain an actual energy E = hf (= f is the*

In fact, Einstein relativistic energy (= E ), relativistic momentum (= p ) cannot explain a photon's energy and momentum, so false.

It is said that the relation of a photon's energy (= E ) and momentum (= p = E/c where c is light speed ) can be obtained by substituting a photon's zero mass (= m_{0} = 0 ) into the relativistic energy-mass-momentum relation. But this is **untrue**.

↑ First of all, if a photon (or light ) with some ( relativistic ) **energy** has **No** mass (← really ? ) as stated by Einstein relativity, the photon **disagrees** with the definition of the relativistic mass (= m ) equal to the relativisic energy (= E ) divided by the square of the light speed c (= relation of m = E/c^{2} is violated only in a photon ! ), which is clearly self-**contradiction** (= Einstein relativity **paradoxically** claims the rest mass of a photon is zero, but the relativistic mass of a photon may not be zero ).

Furthermore, Einstein relativistic energy or momentum relations do **Not** include the **variable** or information about a photon's frequency (= f ) or wavelength (= λ ).

Relavistic energy (= E ) and momentum (= P ) relation contains only the definite constant values such as a photon's zero mass (= m_{0} = 0 = constant ) and the constant light speed v = c, which does Not contain any variables such as frequency f or wavelength λ (= light frequency or wavelength can take many different values, so Not constants ).

This means Einstein relativistic energy-momentum relation can express only one photon or light of only **one constant** energy, because it does Not contain variables or information expressing different light frequencies or different light wavelength.

So it is **impossible** for Einstein relativistic energy-momentum relation to describe actual lights (or photons ) with infinite kinds of **different** energies or momentums.

To be precise, the photon's energy E is proportional to photon's rest mass zero divided by zero (= light speed - light speed ), which photon's energy E = 0/0 is indeterminate and **unable** to designate some physical light (or photon ) energy based on light frequency. So Einstein relativistic energy can**not** define photon energy.

*(Fig.4) A stationary observer K sees an object A moving at a velocity of u _{x} in x direction, which is observed to stop seen by the K' who is moving at the same velocity v = u_{x} as the object A in x direction.*

Here, we actually calculate the relativistic Lorentz tranformation of an object's velocity (= u_{x} = velocity in x direction seen by K, u'_{x} = velocity in x direction seen by K' ) and forces (= F_{y} is the force acting on the object A in y direction seen by K, F'_{y} is the force acting on the object in y direction seen by the moving K' ).

A object is supposed to be moving in x direction at a velocity of u_{x} seen by a stationary K observer, and this same object A appears to stop seen by another observer K' moving in x direction at the same constant velocity v = u_{x} (= temporarily ) as the object A at this point. (= K's velocity v is the constant, but a object's velocity u_{x} is Not constant, because of being accelerated by force in x direction ).

(t,x,y,z) is the time and space coordinate seen by the stationary K observer, and (t',x',y',z') is the time and space coordinate seen by the observer K' moving at a velocity v = u_{x} in the x direction relative to K in the Lorentz transformation.

*(Eq.1) Lorentz transformation and time derivative.*

From the equation of Lorentz transformation, we can obtain the time derivative of the other coordinate's time such as dt'/dt and dt/dt' where t is the time measured in K frame, and t' is the time measured in K' frame.

An object's velocity in x direction seen by K is expressed as u_{x} = dx/dt where x is x-coordinate seen by K.

*(Eq.2) u _{x}' is an object's velocity in x direction seen by K', and u_{x} is an object's velocity seen by K *

An object A's velocity in x direction seen by the moving K' observer is defined as u'_{x} = dx'/dt' where x' t' are the space and time measured in the moving K' frame.

In the same way, an object A's velocity in x direction seen by the moving K observer is defined as u_{x} = dx/dt where x, t are the space and time measured in the stationary K frame.

Using Eq.1, we can obtain Lorentz transformation of an object's velocity ( u_{} → u'_{x} ) as shown above.

*(Eq.3) Lorentz transformation of an object's velocity in y direction between the velocity u' _{y} seen by K' and velocity u_{y} seen by K *

In the same way, using the relation of Eq.1, we can obtain Lorentz tansformation between an object's velocity in y direction seen by K' (= u'_{y} ) and seen by K (= u_{y} ), as shonw above.

K' observer is moving in x direction, so y-coordinates seen by K and K' are the same y = y'.

*(Eq.4) An object A's acceleration in x direction seen by K' (= du' _{x}/dt' ) and seen by K (= du_{x}/dt ) *

Acceleration is defined as the time derivative of an object A's velocity.

Using Eq.1 and Eq.2, we can obtain the relation (= Lorentz transformaion of acceleration ) between the object A's acceleration in x direction seen by the moving K' observer (= du'_{x}/dt' This K' observer is moving at the same speed v = u_{x} as this object at this point, so u'_{x} = 0 ), and an object's acceleration in x direction seen by the stationary K (= du_{x}/dt ).

*(Eq.5) Force (= F _{x} ) equals the time derivative of an object's momentum p*

Force in x direction (= F_{x} ) is defined as the time derivative of an object's (relativistic) momentum p in x direction ( F_{x} = dp_{x}/dt ).

So we can obtain the upper equation of force (= F_{x} ) in x direction in K frame or seen by K ( this p.46 )

*(Eq.6) Force acting on an object A in x direction is the same seen by K (= F _{x} ) and K' (= F'_{x} ), F_{x} = F'_{x} *

In the same way, the force acting on an object A in x direction seen by the moving K' (= F'_{x} ) becomes like the upper figure.

This object A appears to stop seen by the observer K' moving at the same speed as the object, so the object A's velocity is zero u'_{x} = 0 seen by K'

From Eq.5 and Eq.6, we can know that forces acting on an object in x direction does Not change seen by the stationary K (= F_{x} ) or seen by the moving K' (= F'_{x} ). F_{x} = F'_{x} = F_{||} ( this last, this p.15, this last )

It means the force in the x direction (= parallel to the observer K's moving direction) is **unchanged** both in K and K' frames under Lorentz transformation.

*(Eq.7) Lorentz transformation of acceleration of the object A in y direction seen by K' (= du' _{y}/dt' ) and seen by K (= du_{y}/dt )*

Using Eq.3 and Eq.1, we can obtain Lorentz transformation of the acceleration of an object A as seen by the K' moving at the same speed (= v = u_{x} ) as the object A, and as seen by the stationary K ( this p.22 ).

The object A is moving at a velocity u_{x} in x direction (= so velocity in y direction is zero, u_{y} = 0 ) seen by the stationary K, This object A appears to stop seen by the K' observer moving at the same speed (= temporarily, v = u_{x} ) as the object A.

*(Eq.8) *

Force is defined as the time derivative of the object's relativistic momentum p.

Using Eq.7, we can obtain the equation above in this situation.

*(Eq.9) Force in y direction, which is moving in x direction seen by the stationary K (= F _{y} ), appears to be smaller than the force in y direction (= F'_{y} ), which stops seen by the K' observer moving at the same speed in x direction as the object A and its force ( F_{y} < F'_{y} ) *

From Eq.8, we can conclude that the moving force in y direction (= F_{y} ) acting on a moving object A seen by the stationary K appears to be weaker than the force in y direction acting on a stationary object A in y direction (= F'_{y} or F'_{⊥} ) seen by the K' moving in x direction at the same speed as this object A ( this last, this p.15, this last ).

So the force in y direction (= perpendiculat to Lorentz boost direction of K' observer ) acting on the same object appears to increase or decrease depending on the differently-moving observers, which relativistic force causes serious paradox.

2022/11/22 updated. Feel free to link to this site.