Top page (quantum mechanics and Einstein relativity are false )

*(Fig.1) Right-angle lever stops seen by the stationary K due to two equal forces F _{x} = F_{y} 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 ( F_{x} = F_{y} = 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 LFv^{2}/c^{2} 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.

*(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 F_{x} 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/c^{2}, it gives the fictitious hidden momentum of this unreal energy flow injected into one lever arm, which hidden fictitious momentum becomes P = LFv/c^{2} ( 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 = LFv^{2}/c^{2} ( 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 F_{x} point, moving downward (= jagged red line in the upper figure ), and exiting R_{x} 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.

*(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} = F_{x} ), 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.

*(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 (= F_{y} = 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 (= F_{x} = F_{y} ).

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.