﻿ Right angle lever ( Trouton-Noble ) paradox

# Right-angle lever paradox shows special relativity is wrong.

## A stationary right-angle lever seen by the stationary K observer appears to rotate only from the viewpoint of the moving observer K'  ← relativistic unsolvable paradox !

(Fig.1) Right-angle lever stops seen by the stationary K due to two equal forces Fx = Fy applied on it.  ← This same right-angle lever appears to rotate seen only by the moving K', because only F'y force appears to decrease, while F'x force remains unchanged. = two unequal forces only seen by K'  = paradox !

In the upper Fig.1, when two perpendicular equal forces ( Fx = Fy = F ) are acting on a right angle lever's end points at the same distance (= L ) from the pivot, this right angle lever stops or does not rotate, as seen by the stationary K observer due to the zero torque by these two balanced equal forces applied on it.

But as shown on this page, when another observer K' moving in -x direction at a velocity v sees the same right-angle lever, he magically sees this stationary right-angle lever rotating clockwise, because only the force applied on the lever in y direction (= F'y ) appears to decrease, while the force applied on the lever in x direction remains unchanged (= F'x > F'y ) as seen by K' ( this-last,  this p.35,  this p.15 ).

Furthermore, one lever arm's length in x direction is Lorentz contracted as seen by the K' moving in -x direction, while the other lever arm's length remains unchanged, which also increases the imaginary torque of rotating the right-angle lever seen only by K'.

This is clearly one of Einstein relativistic unsolvable paradoxes originating from unphysical relativistic Lorentz tansformation of forces and Lorentz contraction, called "right-angle lever or Trouton-Noble paradox" where one stationary observer K sees the stationary non-rotating right-angle lever, while another moving K' sees the same right-angle lever magically rotating  at the same time.

The rotating torque of the stationary right-angle lever seen by the stationary K is zero (= torque = the sum of force F × the arm's length L = FL - FL = 0 in K frame ).

On the other hand, the torque of the paradoxically rotating right-angle lever seen by the moving K' is Not zero due to the magically-reduced y-force and Lorentz-contracted arm, which rotating torque is equal to LFv2/c2 where v is K' observer's moving speed, and c is the light speed, as shown above.

Several ad-hoc (= wrong ) solutions to this fatal relativistic right-angle lever paradox have been proposed so far, but all of these solutions are based on unscientific assumptions or unreal objects (= as I explain below ), so there is No solution to this paradox, and Einstein relativity is proved to be wrong.

## Unreal energy with hidden momentum P is flowing inside one arm of right-angle lever, causing the unreal counter-torque pulled by unseen nonexistent string connecting the lever and the coordinate's origin ?  ← Relying on "non-existent energy flow" is Not a solution to this right-angle lever paradox.

(Fig.2) Unreal energy flow causing hidden momentum P × fictitious unseen string connecting the origin and right angle lever can generate hidden angular momentum or fictitious counter-torque canceling the right-angle lever rotating paradox ?  ← impossible !

One typical ad-hoc ( wrong ) solution to this rotating right-angle lever paradox relies on unrealistic unseen energy current allegedly flowing inside one arm of the right-angle lever ( this p.3,  this p.2-right-middle ), which can Not be called a right solution at all.

This 8th-last paragraph says
"In his efforts to explain the paradox, Laue invented the concept of the momentum of the “elastic energy current. Laue made the ad hoc assumption that an elastic energy current exists from one end of the lever arm perpendicular to v to the other end of that same lever arm… Laue’s ad hoc postulate and its interpretations appear to raise more questions than they resolve. A few such questions are as follows: What kind of an instrument could one use to detect this elastic energy current in a laboratory ?"

In this ad-hoc wrong solution, they claim that the force F applied on the end point of Fx could (unrealistically) inject the unseen energy current Fv per second into the lever arm downward, only when seen by the moving observer K'.

And this unseen (= unreal ) energy flow called "Laue current" with a uncertain fictitious velocity u could accumulate in one whole arm of the lever whose length is L after the time of L/u.

By converting this fictitious relativistic energy allegedly accumulating in one arm of the right-angle lever into the relativistic momentum through multiplying this hidden energy by the velocity/the square of light speed = u/c2, it gives the fictitious hidden momentum of this unreal energy flow injected into one lever arm, which hidden fictitious momentum becomes P = LFv/c2 ( this lower ).

Furthermore, they baselessly assume some unseen (unreal) string of the changing length vt (= v is the observer K' speed, t is the time ) connecting the stationary origin O (= stationary with respect to the moving observer K' ) and the moving right angle lever causes fictitious angular momentum L = vt × P, and fictitious torque = dL/dt = v × P = LFv2/c2 ( this p.2-right-lower,  this p.4-(7) ) which magnitude is accidentally equal to the rotating torque caused by the reduced y-force and one Lorentz-contracted arm.

Hence, they (falsely) claim that the torque of the paradoxically-rotating right-angle lever would be canceled by this fictitious artificial torque allegedly caused by the unreal energy flow, hidden momentum and unreal string.

But first of all, there is No such thing as this unseen energy flow or hidden momentum.

Force F applied on the lever arm does Not give or inject (fictitious) downward energy into it.

If the force F applied on the lever does not rotate the lever (= this force F applied on A is canceled our by the force applied on B, so No energy injection or flow ), the source generating this force F does Not consume or give energy at all.

And if the right-angle lever starts to rotate by this applied force F, the energy from the force F is used for rotating the lever (= which means paradox occurs ! ) instead of the nonexistent downward energy flowing inside one arm allegedly entering Fx point, moving downward (= jagged red line in the upper figure ), and exiting Rx pivot.

↑ And if the source of force F gives the energy to the lever only when seen by the moving K', and it does not give energy (flow) when seen by the stationary K (= who sees the lever stops instead of moving at v ), this is also paradox !

As a result, there is No legitimate solution to this rotating right-angle lever paradox caused by unrealistic relativistic Lorentz transformation of forces, energies and momentums, so Eintein relativity is intrinsically false.

## Another (wrong) solution tries to replace the original "forces (= F = ma )" by irrelevant "acceleration (= a = removing only the relativistic mass m from the force F )" , which is Not a right torque, hence, Not a solution at all.

(Fig.3) Another wrong solution tries to use only the irrelevant acceleration (= a ) instead of forces (= F = ma where m is the relativistic mass, a is acceleration ) to obtain the (wrong) torque = aL instead of the original torque = FL  ← this is Not a right solution at all.

In another solution, they try to change the original definition of the torque (= T = force F × the arm's length L ), using only the irrelavant acceleration instead of the original forces to obtain the artificially-created (fictitious) torque expressed by the acceleration (= a ) × the arm's length L.

As shown in Fig.1, when we use the original definition of torque equal to the force F × lever arm's length L, this rotating right-angle lever paradox occurs due to non-zero torque seen only by the moving observer K'.

In this wrong solution ( this p.3 ), they unscientifically change the legitimate definition of the torque (= force × length ), and try to use acceleration in x and y directions instead of the forces F in x and y directions.

For example, the force in x direction seen by the stationary K remains unchanged also when seen by the moving K' (= F'x = Fx ), while the acceleration (= a = du/dt, where u is the object's velocity ) seen by the stationary K decreases when seen by the moving observer K' (= acceleration = du'/dt' < du/dt in this case ), because the acceleration does Not consider the (heavier) relativistic mass.

As shown in the above figure, the acceleration lacking the (variable) relativistic mass changes under Lorentz transformation differently from the forces' Lorentz transformation, which could give the zero fictitious toque expressed as the acceleration (= a ) × arm's length (= r ) instead of the non-zero legitimate torque expressed as the force (= F ) × arm's length ( this p.3-(9)-(12) ).

↑ This (wrong) solution uses two different accelerations on one rigid lever, which is meaningless, because the whole rigid lever must rorate or accelerate as one rigid body together at one common acceleration.

↑ Of course, the real torque must be expressed as the applied force × the lever arm's length instead of the acceleration (= without mass ) × the lever arm's length.

So this is Not a right solution, either, due to its wrong definition of torque artificially replacing the force by acceleration.

As shown here, all alleged solutions to this fatal relativistic right-angle lever paradox rely on unrealistic and wrong assumptions, hence, there are No solutions at all.

## Einstein relativity violates "action-reaction law", so false.

(Fig.4) Einstein relativity claims the force in x direction remains unchanged, and only the force in y direction changes by observer's motion in x direction. ← action-reaction law is broken in Einstein relativity !

The point is Einstein paradoxical relativity disagrees with the inviolable fundamental physical principle of "action-reaction law", so Einsten relativity is proven false.

As shown in the upper figure, in the stationary right-angle lever seen by the stationary K observer, two equal forces acting on the end of the arm A cancel each other, and resultantly, this arm A of the right-angle lever remains stationary and does Not rotate.

In this stationary right-angle lever, the force applied on the end of the arm B in y direction (= Fy = F ) is transmitted to the end of arm A, and changed into the counter-force in x direction through the rigid-body right-angle lever and the pivot.

↑ So in the real right-angle lever, due to the action-reaction law, the force applied on arm B in y direction must change into the equal counter-force on arm A in x direction through the rigid right-angle lever and the pivot (= Fx = Fy ).

But the unrealistic Einstein relativistic energy, mass, momentum relation requires only the force in y direction to change depending on the observer's motion, while the force in x direction is unchanged.

↑ This causes serious paradox where only the force applied on the end of the arm B in y-direcion (= action ) decreases and the counter-force (= reaction ) on the arm A in x-direction caused by the y-directional force (= action ) applied on the arm B remains unchanged.  ← only the actional force decreases, and the reactional force remains unchanged.  ← This Einstein relativity clearly violates the action-reaction law, so false.

2022/11/23 updated. Feel free to link to this site.