or taking into account the coulo

NON RELATIVISTIC, NON EINSTEINIAN CARDINAL LAW OF AMPERE OF ELECTRODYNAMICS

^{CRITICAL
PARADOX OF LORENTZ TRANSFORMATIONS, BASIS OF RELATIVITY,
VIOLATING ACTION AND REACTION, SUGGESTION OF THE
EXPERIMENTALLY VERIFIED ORIGINAL LAW OF AMPERE, STRANGELY ENOUGH, IGNORED BY ALL
MODERN BOOKS, UNIVERSITY OR NOT, BOOKS.}

or taking into account the coulomb interaction and the equivalence Ids = qv

ΑΝ V₂=V₁=V BACKWARD AND FORWARD, IN LINE, ALONG TO r₁₂then WE HAVE THE LONGITUDINAL FORCE:

F ₁₂=(-r₁₂q₁q/₂r₁₂³_)(2V²_/c²_{-
3V}²_/c²_{- 1) =}

(-r₁₂q₁q/₂r₁₂³_{)(-
V}²_/c²_{- 1)=}(r₁₂q₁q/₂r₁₂³_)(V²_/c²_{+1), repulsive, as much as twice the coulomb force, for V=c}

ΑΝ V₂=V₁=V SIDE BY SIDE, PERPENDICULAR TO r₁₂thenF ₁₂ = (r₁₂q₁q/₂r₁₂³_)(2V²_/c²_+1),_{REPULSIVE, AS
MUCH AS 3 TIMES THE COULOMB FORCE FOR V=c, for over c, V super-luminal velocity,
(recently compatible), which is allowed by this law, then,}_(2V²_/c²₊₁₎_{TIMES THE COULOMB
FORCE, WHICH IS THE GENERAL CONCLUSION OF THIS LAW.}

LAWS EXPERIMENTALLY
VERIFIED FOR DC CIRCUITS AND SUPPORTED BY HIGH FREQUENCY AC. SEE STIGMA ANTENNA AND PI FRAME, ALWAYS PRESERVING ACTION AND REACTION

PAPPAS' SIX DIMENSIONAL TRANSFORMATIONS:

x'=γ_χ(x-t_χv_χ/c), t_x'=γ_χ(t_χ- xv_x/c²),
with def.: γ_i=(1-(u_i/c)²)^1/2

y'=γ_y(y-t_yv_y/c), t_y'=γ_y(t_y- yv_y/c²)

z'=γ_z(z-t_zv_z/c), t_z'=γ_z(t_z- zv_z/c²)

x²+ y² +z² - t²_x - t²_y- t²_z = x^'2+ y^'2 +z^'2 - t^'2_x - t^'2_y- t^'2_z= s_x²+ s_y²+ s_z²= S²= a constant

^where:x² - t²_x=s_x², y² - t²_y =s_y², z²- t²_z =s_z² ,
with, obviously, s_i=constants

ASSUME : definition of t = (t²_x + t²_y+ t²_z- 2t₀²)^1/2, with t_0, the proper time of a point, i.e. when v_χ= v_y= v_z= 0. When v_χ=v, v_y= v_z= 0, then, the above, with the above definition of t, coincide with the Lorentz Transformations.

So the above, transformations are more general than L.T., PhD thesis of P.T. PAPPAS, "PHYSICS IN SIX DIMENSIONS", Univ. of Athens, 1979.

SIMILARLY, ASSUME R²= x²+ y² +z²-2R₀^2,WHERER₀ IS THE VECTOR MEASURES OF PROPER LENGTH OF THE DIAGONALS OF X_0,Y_0,Z_0,in PROPER t₀ time, I.E., LET PROPER VECTOR R₀= (x, y, z) AND ITS EUCLEDIAN METRIC: R₀²= x²+ y² +z².
Therefore, SIMILARLY R²⁼x²+ y² +z²-2R₀²=x²+ y² +z²-2(x²+ y² +z²) =-x² - y² -z²=-R²^{CONTRADICTION.}

SO, WE CAN NOT MAKE LORENTZ LIKE, RELATIVISTIC TRANSFORMATIONS AMD WITH SPACE , TIME SYMMETRIC A LA EINSTEINIAN IDEAS.

IF, IN CONTRARY AND IN AGREEMENT WITH PAPPAS ABOVE, WE ASSUME: X₀=Y₀=Z₀=R₀=0, in t₀ time, AND CALL R₀=0, ZERO PROPER LENGTH, THEN R²⁼x²+ y² +z²-2R₀²=x²+ y² +z²^,I.E., R= STANDARD PYTHAGORIAN METRIC FOR SPACE,_, IN CONFORMITY WITH THE EUCLEDIAN GEOMETRY FOR SPACE. HOWEVER, FOR TIME, WE HAVE A DIFFERENT NON EUCLEDIAN METRIC: t² = t²_x + t²_y+ t²_z- 2t₀². SO AGAIN, WE CAN NOT FULFILL THE IDEAS OF EINSTEIN OF COMPLETE SYMMETRY, FOR SPACE TO BE ENTIRELY SYMMETRIC TO TIME, BUT APPROXIMATELY SYMMETRIC.

LORENTZ FORCE LAW F, AND LORNTZ TRANSFORMATIONS FOR THE ELECTROMAGNETIC FIELD E,B:

$\mathbf{E} = \frac{q}{4\pi \epsilon_0} \frac{1-v^2/c^2}{(1-v^2\sin^2\theta/c^2)^{3/2}}\frac{\mathbf{\hat r}}{r^2}$

$\mathbf{B} = \mathbf{v} \times \frac{1}{c^2} \mathbf{E}$

F=EQ, F=Q(E+VxB)

F=((r/r²)Qq(1- v²/c²)/4πε₀(1-(v²/c²)sin²(θ))^3/2 + Vx(vxE/c²) =
=(r/r²)(Qq(1- v²/c²)/4πε₀(1-(v²/c²)sin²(θ))^3/2 + Vx(vx

(r/r²)Qq(1- v²/c²)/4πε₀(1-(v²/c²)sin²(θ))^3/2)c²

where $\mathbf{\hat r}$ is the vector pointing from the current (non-retarded) position of the particle to the point at which the field is being measured, and θ is the angle between $\mathbf{v}$ and $\mathbf{r}$ . FOR Θ = 90⁰ F=(r/r²)(qQ/(1- v²/c²)^-1/24πε₀(1- xV/c²),
symbol "x" means the exterior product should be taken, opening the last brackets.

IN GENERAL, NO LONGITUDINAL FORCES. PARALLEL TO VELOCITY V, BUT FOR CHARGED PARTICLES, MOVING SIDE BY SIDE, Θ = 90^0, THE ATTRACTIVE PARALLEL TO r FORCE MAY COME TO INFINITY, INFINITE TIMES BIGGER THAN THE COULOMB FORCE, AND IN GENERAL IT IS NOT TOWARDS THE ACCELERATING FIELD. THIS IMPROBABLE RESULT IS DUE TO THE RELATIVISTIC TRANSFORMATIONS OF THE FIELDS. WHETHER TRUE OR NOT, CAN NOT BE KNOWN TO AN ORDINARY LABORATORY, WITH NO HIGH RELATIVISTIC VELOCITIES AVAILABLE. IT SHOULD BE KNOWN TO CERN, WORLD BIGGEST ACCELERATOR'S LABORATORIES IN SWITZERLAND.
THE CERN IS KINDLY QUESTIONED ACCORDINGLY.

LAWS EXPERIMENTALY INDISTINGUISHABIE, FOR FAST MOVING PARTICLES, IN A NORMAL LABORATORY.
SET SO TO PLEASE RELATIVITY AND EINSTEIN.

THE CERN IS KINDLY QUESTIONED ACCORDINGLY.
FORCE IN RELATIVITY:look at the end CLICK HERE

P.T.P.

When $v^2 \ll c^2$ , the electric field and magnetic field can be approximated as^[4]

$\mathbf{E} =\frac{q}{4\pi\epsilon_0}\ \frac{\mathbf{\hat r}}{r^2}$ 、

$\mathbf{B} =\frac{\mu_0 q \mathbf{v}}{4\pi} \times \frac{\mathbf{\hat r}}{r^2}$

EXPERIMENTALLY VERIFIED.

END