﻿ Lorentz force law incompatibility with special relativity, electromagnetic paradox

Einstein special relativity contradicts electromagnetic Lorentz force law. No solution to this true paradox.

Einstein relativistic Lorentz transformation unrealistically changes magnetic field into the electric field by changing the neutral wire into the electrically-charged wire depending on observers' motions.  ← paradox !

(Fig.1) A stationary observer K sees the neutral wire (= charge density ρe = 0 ) with electric current Jx generating magnetic field B, which is magically seen as the electrically-charged wire (= whose charge density ρe' is Not zero ! ) generating the electric field E' from the viewpoint of a moving observer K' !

In fact, Einstein (special and general) relativity contradicts the experimentally-verified electromagnetic theory.

In the upper figure, the electric current Jx is flowing in the -x direction (= here we assume positive charges are flowing as electric current, and negative charges are fixed at definite positions for simplicity ) inside the electrically-neutral wire, and it generates the magnetic field (= in the y direction above the wire ) around it.

A stationary observer K sees an external positive charge (= + ) at rest above the neutral wire.  ← This stationary positive charge outside the wire remains at rest because it feels No Lorentz magnetic force (= because this charge stops, Lorentz magnetic force = evB = 0, where the outside positive charge's velocity v is zero seen by K ) or No electric forces from the neutral wire.

But from the viewpoint of another observer K' who is moving in the x direction at a velocity v, this K' sees the same external positive charge (= stationary seen by the stationary K observer ) moving in the -x direction at a velocity v, because Einstein unphysical relativity adopts No absolute space or No absolute motion (= all motions are supposed to be relative ).

So this external positive charge appearing to be moving experiences Lorentz magnetic force downward ( this p.2 ) seen only by K', which means this external positive charge may be paradoxcically moving downward seen only by K', while the stationary observer K sees this same positive charge stopping (= Not moving downward ) !

↑ To solve this paradox, Einstein relativity unreasonably claims that the neutral wire (= seen by the stationary K ) should magically change into the electrically-positive charged wire as seen by the moving K', and this magically-positively-charged wire generates the (fictitious) electric field (= Ez' ) upward in the z direction, and this (fictitious) electric field upward could cancel the Lorentz magnetic force downward, and after all, both K and K' see the same external positive charge remaining at rest in the z direction.

So in the unrealistic Einstein's relativistic world, the mere observer's motion can magically change the originally-neutral wire with No electric field into the electrically-charged wire generating (fictitious) electric field E !

According to relativistic electromagnetic theory, under Lorentz transformation, the electric (= E ) and magnetic (= B) fields seen by the static K observer in the space time (t,x,y,z) must magically change into the completely different electric (= E' ) and magnetic (= B') fields seen by the moving observer K' in the spacetime (t',x',z',y').  this p.14,  this p.14,  this p.17

In the same way, under Lorentz transformation, the charge density ( = ρe ) and electric current density (= J ) seen by the stationary observer K must be changed into the completely different charge density (= ρ'e ) and electric current density (= J' ) seen by the moving observer K' like the relativistic spacetime ( this p.2-3,  this p.3,  this box-13.5,  this p.8 ).

↑ So the new (unrealistic) positive or negative charge (density) ρe' can be generated from the originally-neutral wire (= J ) only by being seen from differently-moving observers according to the fictional Einstein relativity.

This ad-hoc relativistic solution relying on fictitiously-generated charges cannot eliminate the true relativistic electromagnetic paradox, after all.

Einstein relativity can Not solve its true electromagnetic paradox, so false.

(Fig.2) An external negative charge (= - ) is Not attracted toward the neutral wire seen by the stationary observer K, but the same negative charge appears to be attracted and moved closer to the same wire magically transforming from the electrically-neutral to positively-charged seen by the moving observer K' = this is true unsolvable paradox

In fact, Einstein relativistic theory cannot solve its true electromagnetic Lorentz transformation paradox, so the relativity incompatible with the experimentally-verified electromagnetism is completely wrong.

As shown in Fig.1, the neutral wire with electric current seen by the stationary K observer magically appears to be positively-charged seen by the moving observer K.

When there is an external negative charge (= - ) at the left or right side of the horizontal electric wire, this external negative charge not attracted to the neutral wire seen by K paradoxically appears to be attracted to the (unrealistically) positively-charged wire seen by the moving observer K', as shown above.

This is one of true relativistic paradoxes which can never be solved (= so this true paradox is rarely seen in textbooks ).

As shown above, this external negative charge is paradoxically attracted and moved toward (= x direction ) the wire with current flowing in the x direction.
Lorentz magnetic force, which is always perpendicular to the charge's moving direction, cannot cancel this paradoxical electric attraction (= even if the magnetic force is generated, its direction could be in y or z direction, Not in the x-drection of electric attraction ), which means this paradoxical electrical attraction only seen by K' remains unsolved.

This fatal relativistic paradox originates in the intrinsically-flawed relativistic Lorentz transformation of the electromagnetic field E.

According to the relativistic Lorentz transformation of electromagnetic field, the electric field (= Ex or E|| ) in x direction (= K' moving direction ) must remain unchanged or zero (= Ex = Ex' = 0 ) also seen by the moving observer K' ( this p.14,  this p.14 ).  ← This Lorentz transformation of electric field is clearly wrong.

As shown in Fig.1 and Fig.2, the originally zero electric field (= Ex = 0 ) seen by the stationary observer K clearly changes into the non-zero electric field Ex' due to the newly-appearing positive charges in the electric wire seen by K' (= charge density ρ' seen by K' is Not zero,  this p.3 ).

These electromagnetic paradoxes are caused by the Einstein relativity rejecting some absolute frame or space, where all the motions must be relative, illusion.

These electromagnetic paradox can be easily solved, if we admit some realistic medium where the Lorentz magnetic force is generated only when an charged particle such as an electron is moving relative to some "medium" generating de Broglie wave, regardless of which observer, stationary or moving, is seeing it.

Electromagnetic Lorentz force law is incompatible with special relativity.

[ "Trouble with Lorentz force law: incompatibility with special relativity" by Mansuripur paper has Not been resolved. ]

(Fig.3) A stationary neutral wire seen by the stationary K observer appears to be magically electrically-charged and rotated under applied electric field E seen by the moving observer K' = This is one of true unsolvable relativistic paradoxes !

The recent Mansuripur's paper "Trouble with the Lorentz Law of Force: Incompatibility with Special Relativity and Momentum Conservation" published in Phys.Rev.Lett (108, 193901 2012 ) saying "Textbook electrodynamics may contradict relativity." is one of these true relativistic electromagnetic paradoxes.

In the upper Fig3, the electric current I (= here positive charges are supposed to be flowing and negative charges are fixed at their positions ) is flowing inside the electrically-neutral rectangularly looped wire under the external electric field E in the x direction seen by the stationary observer K.

Of course, this electrically-neutral wire (= whose charge density ρe = 0 ) is Not moved or rotated under applied electric field E seen by the stationary observer K.

But according to the unscientific Einstein relativistic Lorentz transformation, the upper wire of this same electrically-neutral circuit seen by the stationary K appears to be positively-charged, and the lower wire of this same circuit appears to be negatively-charged seen by another observer K' moving in x direction at a velocity v ( this p.6 ).

So the same stationary neutral wire (= through which electric current I is flowing ) seen by the stationary K observer appears to be paradoxcially rotated clockwise under the applied electric field E seen by the moving observer K' at the same time.

↑ this is clearly one of true relativistic unsolvable paradoxes, because two differently-moving observers K and K' see the same wire under the external electric field E at the same time, but K sees the wire neutral and stationary, and K' sees the same wire electrically-charged and rotated.

This rotating torque (= T ) of the magically-charged wire under the external electric field E is expressed as the rotating radius (= a/2  × 2 = a ) × the electric force F between the external electric field E and the upper positive charges (= charge density ρ'up × the upper wire's (Lorentz-contracted) length b ) or the lower negative charges (= charge density ρdown' × the lower wire's (Lorentz contracted) length b ).

The net torque of this electrically-charged rectangular wire being rotated by the electric field E seen by the moving oberver K' equals EIabv/c2 where v is the speed of K' and c is the light speed, as shown above.

The alleged solution to this relativistic Lorentz force paradox is wrong.   ← No solution !

[ The alleged solution to relativistic Lorentz force paradox uses unrealistic "hidden momentum", which is scientifically wrong. ]

(Fig.4) Positive charges in the current are accelerated like "free particles (← wrong assumption)" under the applied electric field E, and gain the heavier relativistic mass (= hidden momentum ? ) despite their velocity V being unchanged ?  ← contradiction !

All the alleged solutions to this true relativistic paradox incompatible with the electromagnetic Lorentz force law try to use unrealistic momemum called "hidden momentum ( this lower,  this 18th-paradox )."

↑ This "hidden momentum" used to solve the unsolvable relativistic paradox is unrealistic and unavailable as a legitimate solution.

In this rotating wire case, this hidden momentum corresponds to the increased momentum gained by the positive charges in the current accelerated by the external field E in the x direction treated as fictitiously-free particles, and this hidden momentum is unrealistically in the z direction (= despite being accelerated by the electric field E in the x direction, so contradiction ) gained by accelerated positive charged moving in the z direction inside the right-side wire.

↑ There is No external force applied in the z direction in this case, hence, this hidden momentum P in the z direction under the external electric field E in the x direction contradicts the physical principle, and wrong (= positive charges accelerated by the external electric field E in x direction hit and bounce back from the wall of the wire when turning into z direction = total momentum in z direction combining rebounded accelerated changes and wire's wall should be zero, hence No hidden momentum in z direction ! ).

Furthermore, electric charges are Not acclerated (= hence No hidden momentum is acquired by charges ), because the applied electric field E is canceled out by accumulated charges in a wire.

In this alleged solution, they falsely assume that positive charges in the electric current are accelerated in the x direction by the applied electric field E like "free particles" (← this is one of wrong assumptions ), and this accelerated charges allegedly get heavier due to its heavier relativistic mass (= as a charged particle's velocity V is higher, the relativistic energy and mass become larger ).

↑ Each positive charge is accelerated under the applied electric field E and allegedly gains the additional energy = qEb (= q is each charge, b is the length of wire in x direction ), and its relativistic mass increases by qEb/c2 which is equal to the increased relativistic energy Δmc2 = qEb divided by the square of light speed c, c2 (= qEb)/c2.

As a result, the total gained hidden momentum of positive charges accelerated by the applied electric field E becomes qEb/c2 (= each charge q's increased relativistic mass ) × V (= each charge's constant speed = this is another wrong assumption ) × λ (= particle density per length ) × a (= length of the right or left z-directional wire ) = EIab/c2 ( this p.1-(1) which paper's hidden momentum P is in y direction and the external electric field is in z direction ) where the electric current I is expressed as qλV.

But this solution using (unreal) hidden momemtum is based on the wrong assumption that each accelerated charge q gains the additional relativistic energy or mass, but this charge q's velocity V (or v ) remains the unchanged constant V between the left (= before acceleration ) and right-side (= after acceleration by E ) wires as shown in this p.1-left-(1) equation using the common single charge's velocity v.

Because when assuming both the left and right wires remain the electrically-neutral (= positive charge's numbers are the same both in the left and right wires ), and the same electric current I is flowing in the left and right wires (= if this electric current I are different, charges accumulate in some points ), each charge q's velocity V must be the same both in non-accelerated left wire and accelerated right wire, which is clearly contradictory.

So this solution is invalid, and they cannot explain the contradiction of why the whole wire could gain the hidden momentum P in the z direction under the external electric field E in the x direction.  ← this is impossible.

No hidden momentum, so No solution to relativistic paradox !

[ Accumulated positive charges by electric field E cancel the electric field E, hence, electric charges are Not accelerated, and No hidden momentum is produced. ]

(Fig.4') Applied electric field E positively charges the right side of the wire to cancel its electric field.  ↓

In fact, electric (positive) charges neither get accelerated nor increase ad-hoc hidden momentum in the applied electric field E.

Because when we apply the electric field E (= in the right direction ) in the neutral wire, positive charges tend to accumulate in the right-side wire and eventually cancel the applied electric field E, as shown in the upper figure-right.

So the (positively) charged particles in the electric current are Not accelerated even in the applied electric field E, hence, No (hidden) momentum is obtained by flowing electric charges.

As a result, there is No solution to this true relativistic Lorentz magnetic foece paradox, and Einstein relativistic theory is false.

This wrong solution (p.1-left) says "The external electric field does a positive work on the charges moving to the right and a negative work on the charges moving to the left in the figure, such that if the energy of the charges going down is U, the energy of the charges going up (= hidden momentum increases ) is U + qEb.."  ← This does Not happen in actual electric wire.

Hidden momentum solution needs the unrealistic angular momentum and torque.

(Fig.5) Solution to the paradox relies on unreal angular momentum and torque caused by "unseen nonexistent string" connecting the moving observer K' and the center of the wire.

The alleged solution to the relativistic electromagnetic paradox needs not only the unscientific hidden momentum (= this was disproven, though ) but also the unrealistic angular momentum or toque caused by an unseen nonexistent string (= whose length is changing like vt where v is the observer K's velocity and t is the time ) connecting the moving observer K' and the center of the wire (= of course, there is No such thing as unseen string between the observer K' and the center of the wire ), as shown above.

They unreasonably claim there is some hidden (unrealistic) angular momentum expressed as the hidden momentum P × the distance (= vt ) between the moving observer K' and the center of wire (← This ad-hoc hidden angular momentum does Not exist ).

And the (unrealistic) hidden torque (= T ) is expressed as the time derivative of this hidden angular momentum, which becomes T = EIabv/c2 = Em0v/c2 (= in this paper-p.1-right uses m0 = Iab, and torque is x direction ), which artificial torque is accidentally equal to the toque of the rotating wire by the newly-appearing electric charges pulled or pushed by the external electric field E.

So they claim that the torque of (paradoxical) rotating the electrically-charged wire in the applied electric field E seen by the moving observer K' is used for increasing the unrealistic hidden angular momentum (= L ) expressed by the hidden momentum P × vt (= distance between the moving observer K' and the center of the wire allegedly connected by non-existent string ), hence, the paradoxical rotation of the wire does not happen from the viewpoint of the moving observer K', either.

↑ This ad-hoc assumption used in the alleged solution based on unphysical hidden momentum, unseen string and unrealistically charges behaving like free particles is completely wrong, so there is No legitimate solution to this relativistic paradox.

First of all, this unrealistic hidden angular momentum or torque allegedly caused around the moving observer K' (= fictitious rotating center ) has nothing to do with the torque of the wire rotated around the center of the wire by the applied electric field E (= these two trorques use completely different centers of rotation, one is the center of the wire, and the other uses the moving observer K' as the fictitious center of rotation ).

Another (wrong) solution using unreal hidden momentum to the relativistic paradox.

(Fig.6) This solution uses the impossible assumption that the right-side wire becomes negatively-charged against the direction of the applied electric field E !

Another solution also uses the same kind of the (unreal) hidden momentum caused by the positive charges in the current accelerated by the applied electric field E (= this assumption proved to be wrong, as I said ) like free particles.

The problem is this solution is based on the impossible assumption that the right-side wire becomes negatively-charged against the direction of the external electric field E ( in this picture, the upper wire with smaller number of positive charges means the upper wire becomes negatively-charged against the direction of the electric field E in the upper direction,  this p.2 ).

↑ This assumption is scientifically wrong, because under the applied electric field E in the x (= right ) direction, the right wire tends to be positively-charged instead of the negatively-charged !

In order to generate the uniform (= constant ) electric current I both in the left (= decelerated postive charges' flow ) and right wires (= accelerated positive charges' flow ), the number of flowing positive charges with higher velocities in the right wire must be smaller than the slower charges in the left wire, which means the right-side wire becomes unrealistically negatively-charged against the applied electric field E, which is impossible.

This constant uniform electric current I is equal to qNtvt/a (= Nt is the total righ-wire's charge's (smaller) number and vt is each charge q's (higher) velocity in the right wire ) = qNbvb/a (= Nb is the total left-wire's charge's (larger) number, and vb is each charge's (lower) velocity in the left wire ), "a" is the length of the wire in the z direction.

The right-wire's charges have the higher total momentum due to its heavier relativistic mass and higher velocity caused by the increased relativistic energy by the electric field's acceleration (= each positive charge gains more energy = qEb in the right side wire.  ← this assumption used in solution proved to be wrong, as I said ).

As a result, the (unreal) hidden momentum P of the whole wire becomes the same ( this p.2-(12) ) as the first solution, and the same (unreal) angular momentum and torque around the completely-irrelevant observer K' must be used to cancel the rotating wire paradox ( this p.3-(15)-(17) ).

Conclusion:  There is No solution to the relativistic electromagnetic paradox.

(Fig.7) Hidden momentum is impossible, because positive charges in the electric current tend to accumulate in the right wire due to the applied electric field E, and this accumulated positive charges in the right wire cancel the external electric field E, hence, each charge q is Not accelerated like free particles, and No hidden momentum by the accelerated charges' momentum is generated !

All the alleged solutions as shown in Fig.4 and Fig.6 are based on the unscientific and impossible assumption that the positive charges in the electric current are "accelerated" like (fictitous) free particles by the externally-applied electric field E in the x direction, hence, the right-wire contains more accelerated positive charges with more (hidden) momentum.

But when we think about this case realistically, under the externally-applied electric field E in x direction, the positive charges tend to accumulate in the right wire due to the applied electric field E, and eventually those accumulated positive charges in the right wire cancel the external electric field E.

This means the positive charges eventually get to flow at the uniform constant speed without being accelerated by the applied external electric field E which have been canceled and counteracted by the accumulated positive charges.

No accelerated charges means No hidden momentum in the right wire, hence, all the alleged solutions exploiting the (unreal) hidden momentum and hidden torque are invalid.

As a result, Einstein relativity clearly contradicts the experimentally-verified electromagnetic theory, hence, wrong.

No hidden momentum, because electrical charges are Not free particles.

(Fig.8) Electrical charges eventually flow as a uniform current interacting with each other via Coulomb force, hence, No hidden momentum caused by accelerated charges.

First of all, electric charges inside the electric current are Not free particles, they are constantly interacting with each other via Coulomb electric field.

So the hidden momentum caused by the charges accelerated by the applied electric field like (fictitious) free particles is impossible.

↑ Even if this unrealistic hidden momentum P is generated by being accelerated under the applied electric field E in the x diretion, these accelerated positive charges would collide with the wall of the wire at the corner and change their moving direction, which collisions push the whole wire in the same x direction as the external electric field E in x direction instead of the z direction used in the wrong solution.

As a result, Einstein relativity with fatal unsolvable paradox is proven to be a wrong theory.

appendix

electric Lorentz transformation (old)

2022/11/19 updated. Feel free to link to this site.