Re: SR inconsistent?

From: David Rutherford (drutherford_at_softcom.net)
Date: 08/12/04 

Date: Thu, 12 Aug 2004 16:17:04 -0700

J.J. Simplicio wrote:
>
> OK. It's a bit messy and there are likely to be typos. But, hopefully you
> will check the calculations.
>
> In K there is a uniform electric field E in the y-direction. Let u be the
> speed of K' relative to K. Transforming to K', the only nonzero components
> of the fields are (setting c = 1)
>
> E'_y = G E
>
> B'_z = -G u E
>
> where G is an abbreviation for 1/Sqrt(1 - u^2).
>
> Then the components of the Lorentz force are
>
> F'_x = q V'_y B'_z = -G q E u V'_y
>
> F'_y = q(E'_y - V'_x B'_z) = G q E (1 + uV'_x)
>
> The equations of motion are (with m = rest mass)
>
> d (m V'_x / Sqrt(1-V'_x^2-V'_y^2) /dt' = -G q u E V'_y
>
> d (m V'_y / Sqrt(1-V'_x^2-V'_y^2) /dt' = G q E (1 + uV'_x)
>
> With various manipulations these two equations may be solved for the
> acceleration components:
>
> d V'_x /dt' = -A Sqrt(1-V'_x^2-V'_y^2) V'_y (u+V'_x)
>
> d V'_y /dt' = A Sqrt(1-V'_x^2-V'_y^2) / (1-V'_x^2) *
>
> [1 - V'_x^2 - V'_y^2 (1 - uV'_x -V'_x^2) ]
>
> Here, A stands for the constant GqE/m.
>
> The initial conditions are
>
> V'_x = -u and V'_y = 0 at t' = 0.

I've don't have time right now to go through all of your calculations,
but right off, I see a problem. V'_y is not zero at t' = 0 because V_y
is not zero in F at t = 0. The charge is in motion along the y-axis at t
= 0. If V_y and V_y' were zero, I'd agree with you, since qV'xB' would
be along the y'-axis and there would be no component of the net force in
F' along the x'-axis, but since V' has a component in the y'-direction
in F', qV'xB' has a component in the x'-direction in F'. 

-- 
Dave Rutherford
"New Transformation Equations and the Electric Field Four-vector"
http://www.softcom.net/users/der555/newtransform.pdf
Applications:
"4/3 Problem Resolution"
http://www.softcom.net/users/der555/elecmass.pdf
"Action-reaction Paradox Resolution"
http://www.softcom.net/users/der555/actreact.pdf
"Energy Density Correction"
http://www.softcom.net/users/der555/enerdens.pdf
"Proposed Quantum Mechanical Connection"
http://www.softcom.net/users/der555/quantum.pdf

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