Top ( quantum mechanics and Einstein relativity are wrong )
(Fig.1) a thing of rest mass m0 moving at a velocity (= ux ) in x direction seen by a stationary observer K experiences forces (= Fx in x direction, Fy in y direction ). ← This thing appears to stop seen by a observer K' moving at the same velocity v = ux as the thing. Force in y direction seen by K' (= F'y acting on a thing at rest ) is bigger than the y-force seen by K (= Fy acting on a moving thing is smaller ), which causes paradox !
Einstein relativity introduced the artificial relativistic energy E, relativistic momentum p and relativistic mass of a thing, which could be magically heavier or lighter depending on the observer's motion, even without touching or adding additional mass to the observed thing.
In order to use this paradoxical relativistic energy, momentum and mass together with the relativistic Lorentz transformation, the actual force (= F ) acting on a thing must be unrealistically change depending on observers seeing it, which causes serious paradox, hence the relativistic energy, mass, momentum relation is wrong.
On this page, we explain this fatal paradox of Einstein relativistic energy, mass, momentum and force relation in detail.
In the upper figure, a thing of a rest mass m0 is moving in the x direction at a velocity ux seen by a stationary observer K.
This same thing moving seen by K appears to stop as seen by another observer K' moving in the x direction at the same velocity v = ux as the thing (= K' is the rest frame of this moving thing ).
Forces are constantly applied on this thing in x (= Fx ) and y (= Fy ) directions.
According to special relativistic Lorentz transformation of forces, this forces (= actual forces F can be defined as the time derivative of the relativistic momentum p ) in y direction (= Fy or F⊥ = force perpendicular to the moving direction of K' observer ) must magically decrease, when the force is applied on a thing moving, compared to the force acting on the thing at rest (= F'y Fy < F'y, this p.30.35, this last, this p.15, this last, this p.5 ).
This unphysical change of actual forces (= actual Newtonian three-forces = Not artificially-defined fictitious relativistic four-force ) seen by differently-moving observers cause the serious paradoxes, so the relativistic energy, mass and momentum relation based on this unrealistic (relativistic) forces are self-contradictory and false.
(Fig.2) A stationary K observer sees a rectangular loop rail at rest which experiences two balanced forces = a stationary force Fy upward and a moving force Fy of the same magnitude downward (= thing exerting this moving downward force Fy is sliding in x direction on the lower rail ). But another moving observer sees this same loop rail paradoxically moving downward, because the magnitudes of two applied forces F'y appear to be different and unbalanced seen only by K' !
Special relativity demands that forces acting (= Fy ) on a thing at rest in y or z direction must decrease when a thing (and a force acting on it ) is moving in x direction, or when seen by a observer moving in x direction relative to a thing or force ( this last, this last, this p.35, this p.45 ).
This relativsitic unrealistic Lorentz transformation of forces causes serious paradox, and shows Einstein relativity and its ad-hoc relativistic energy, mass, momentum relation founded on this unrealistic forces' Lorentz transformation are false, which must be immediately replaced by the realistic Maxwell equation which first showed the particle or light energy equals the momentum multiplied by light speed c or mc2, which authentic Maxwell E = mc2 was copied and modified by unphysical Einstein relativity in the wrong way.
In the upper figure, an rectangularly looped rail is at rest seen by a stationary observer K, when two forces with the same magnitude (= Fy ) are applied on it in the opposite direction where one force at rest is upward, the other force downward is moving in the x direction at a velocity v (= this source exerting the downward force is sliding and moving on the lower rail of the loop in the x-direction ).
Another observer K' is moving in x direction at the same velocity v as the downward-force source, so this K' sees the loop rail moving in the opposite -x direction at a velocity of v, and K' sees the the downward force sliding on the lower rail (= seen by K ) appearing to stop.
According to relativistic Lorentz transformation of forces, a force in y direction moving in x direction appears to decrease compared to a stationary force in y direction.
Hence, the magnitude of upward force which appears to be moving in -x direction seen by the moving K' observer decreases from its original magnitude Fy seen by the stationary K observer.
On the other hand, the magnitude of the downward force which appears to stop seen by the moving K' appears to increase from the original force seen by the stationary K.
As a result, two forces of the same magnitude acting on the loop rail in the opposite direction seen by K become magically different in their magnitude seen by K', and this originally-stationary loop rail under two balanced equal upward and downward forces appears to be accelerated and moving downward seen only by K' due to the unbalanced unequal upward and downward forces.
This is clearly one of true paradoxes of Einstein relativity or relativistic energy, mass, momentum relation.
Because two differently-moving obsevers K and K' see the same one rectangular loop rail, and one of them sees it stop due to two same-magnitude balanced forces applied on it, and the other observer sees it magically moving downward due to two forces with different magnitudes applied on it
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 (= m0 = 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 variable of light frequency, Not the constant ) of photon (or light).
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 (= m0 = 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/c2 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 (= m0 = 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 cannot define photon energy.
(Fig.4) A stationary observer K sees an object A moving at a velocity of ux in x direction, which is observed to stop seen by the K' who is moving at the same velocity v = ux as the object A in x direction.
Here, we actually calculate the relativistic Lorentz tranformation of an object's velocity (= ux = velocity in x direction seen by K, u'x = velocity in x direction seen by K' ) and forces (= Fy 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 ux 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 = ux (= temporarily ) as the object A at this point. (= K's velocity v is the constant, but a object's velocity ux 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 = ux 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 ux = dx/dt where x is x-coordinate seen by K.
(Eq.2) ux' is an object's velocity in x direction seen by K', and ux 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 ux = 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 uy 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 (= uy ), 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 (= dux/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 = ux as this object at this point, so u'x = 0 ), and an object's acceleration in x direction seen by the stationary K (= dux/dt ).
(Eq.5) Force (= Fx ) equals the time derivative of an object's momentum p
Force in x direction (= Fx ) is defined as the time derivative of an object's (relativistic) momentum p in x direction ( Fx = dpx/dt ).
So we can obtain the upper equation of force (= Fx ) 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 (= Fx ) and K' (= F'x ), Fx = 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 (= Fx ) or seen by the moving K' (= F'x ). Fx = 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 (= duy/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 = ux ) as the object A, and as seen by the stationary K ( this p.22 ).
The object A is moving at a velocity ux in x direction (= so velocity in y direction is zero, uy = 0 ) seen by the stationary K, This object A appears to stop seen by the K' observer moving at the same speed (= temporarily, v = ux ) 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 (= Fy ), 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 ( Fy < F'y )
From Eq.8, we can conclude that the moving force in y direction (= Fy ) 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.
