Mathematical argument
against the validity of
the Voigt transformations.
[ part 2 of 2 ]

The actual problem has specifically to do with both frames being stationary after the one frame has completed moving. This is where the problem is. Adding motion in, is post aut propter, to this completely mathematical challenge. That is, if we substituted D for distance, to replace VT, then the mathematically inequality would still be generated in X' = X - D
                      


CASE 4
Voigt coordinate point transformation...moving a frame to the right by

              

       
       
       

Where four art thou ...

in , art thou the length going from backwards to ?
The mechanics of Voigt's transformation are shown by the smaller green arrow.
  


12 , 13, 14, 15, 16, 17,
in a coordinate length of   must commence from
is not at instead is at
in neither nor determine coordinate lengths in
to      to     



or, in , art thou the length going from to ?

Voigt's "proof" that the transformation was done correctly.
 

in     
does not commence from instead it commences from
in
Voigt never assigns a point name for the transformed point in frame. It must called X' - to match the points' coordinate value.
to      to     


coordinate X' = coordinate X - coordinate VT



Since the two shorter line segments have the same total length as the longest one. We are led to believe that the transformation was done correctly, It is not at all obvious then why his "proof" is wrong...as certainly the lengths of those line segments do add up properly.


Voigt should not be transforming the line segment length of . The task was to determine the corresponding coordinates for a point at to the right by 7.


Granted, this point in has an abscissa in its' moved to frame of . However, the line segment length of completely FAILS to have an abscissa in the corresponding unmoved frame .


ALL X coordinate lengths start counting from 0,0,0 in their own frame. Voigt however, starts his length in at VT,0,0. No can do. is not an origin in . Nor is he allowed to select as an origin in to establish his length by counting backwards towards either VT,0,0 or to 0,0,0 in the unmoved frame.


moved to the right correctly
coordinate X' = coordinate X + coordinate VT




moved to the left correctly
coordinate X' = coordinate X - coordinate VT





Below, Voigt has one constant    which has 2 different values being possible...no can do.
       AND          


Given a point at 11,0 then the correct coordinate transformation to the right by 7 is
18,0     not 4,0      not ( 11,0 - 7,0 )

Given a point at 11,0 then the correct coordinate transformation to the left by 7 is
4,0



This is the missing ten bucks...

Voigt's vt length must be added and not subtracted from the x length


Additionally, it is questioned why only an ( X,0,0 ) is allowed and not ( X,Y,Z )
What if we wanted to transform to a new origin at 1,2,-5...all these points originally at (2,3,15) and (6,-2.5,3.4) and (0,-5,-2.34).



Quite simply, due to it being a strictly mathematical process, then the

        is merely       


Conclusion - the Voigt transformations were malum in se in 1887 and are still wrong today and cannot be used as a proper basis for the accepted Theory of Relativity. Correspondingly, the validity of both time dilation and length contraction are reductio ad adsurdum. Without the Voigt equation, Relativistic conclusions are unsubstantiable.
copyright    steve waterman    december 29, 2008    all rights reserved