Dirk Van de moortel wrote:
> "Golden Boar" <goldenboar@hotmail.com> wrote in message
> news:1160226593.247248.77960@i42g2000cwa.googlegroups.com...
> >
> > Dirk Van de moortel wrote:
> >> "Golden Boar" <goldenboar@hotmail.com> wrote in message 
> >> news:1160225545.632563.120320@i3g2000cwc.googlegroups.com...
> >> >
> >> > Dirk Van de moortel wrote:
> >> >> "Golden Boar" <goldenboar@hotmail.com> wrote in message 
> >> >> news:1160218752.188077.207720@h48g2000cwc.googlegroups.com...
> >> >>
> >> >> [snip]
> >> >>
> >> >> >> >> >> >> >> >> "Golden Boar" <goldenboar@hotmail.com> wrote in message
> >> >> >> >> >> >> >> >> news:1159971408.504933.294930@m73g2000cwd.googlegroups.com...
> >> >>
> >> >> > Does anyone know the equations for the Lorentz transformations when the
> >> >> > velocity is not along the x-axis only. I have been searching the
> >> >> > internet, but with no success, so I have attempted to derive these
> >> >> > equations myself, and have came up with the following:
> >> >> >
> >> >> > t' = c.(t - v.sqrt(x^2 + y^2 + z^2) / c^2) / sqrt(c^2 - v^2)
> >> >> > x' = c.(x - x.v.t / sqrt(x^2 + y^2 + z^2)) / sqrt(c^2 - v^2)
> >> >> > y' = c.(y - y.v.t / sqrt(x^2 + y^2 + z^2)) / sqrt(c^2 - v^2)
> >> >> > z' = c.(z - z.v.t / sqrt(x^2 + y^2 + z^2)) / sqrt(c^2 - v^2)
> >> >> >
> >> >> > where, gamma = c / sqrt(c^2 - v^2)
> >> >> >
> >> >> > Can someone tell me if these equations are valid?
> >> >> >
> >> >>
> >> >> Listen carefully now. These are the rules of the game:
> >> >>
> >> >> There are two systems with parallel spatial coordinate axes.
> >> >> The origin of one of the systems has a given velocity V w.r.t.
> >> >> to the other system. V is a vector in some arbitrary direction.
> >> >> The vector has components ( vx, vy, vz ) as seen in one of the
> >> >> frames.
> >> >>
> >> >> Don't ask how these numbers are calculated. They are given.
> >> >>
> >> >> They specify the direction and the magnitude of the velocity.
> >> >> You asked for "the equations for the Lorentz transformations
> >> >> when the velocity is not along the x-axis only".
> >> >> The velocity having given components ( v, 0, 0 ) expresses
> >> >> that the velocity is along the x-axis.
> >> >> The velocity having given components ( vx, vy, vz ) expresses
> >> >> that the velocity is not along the x-axis.
> >> >> In the latter case the magnitude of the velocity is
> >> >>     sqrt( vx^2 + vy^2 + vz^2 )
> >> >> and this number is given the letter v.
> >> >>
> >> >> In general, an arbitrary point with coordinates
> >> >>     ( x, y, z ) = ( x1, y1, z1 ) in the unprimed frame.
> >> >> has coordinates
> >> >>     ( x', y', z' ) = ( x1', y1', z1' ) in the primed frame.
> >> >> and, taking time into the picture, an arbitrary event with coordinates
> >> >>     ( t, x, y, z ) = ( t1, x1, y1, z1 ) in the unprimed frame.
> >> >> has coordinates
> >> >>     ( t', x', y', z' ) = ( t1', x1', y1', z1' ) in the primed frame.
> >> >>
> >> >> A coordinate transformation allows you to calculate the numbers
> >> >> ( t', x', y', z' ) when the numbers ( t, x, y, z ) and the velocity
> >> >> are known. In this case the velocity is given by the vector V
> >> >> with components ( vx, vy, vz ) and magnitude
> >> >>     v = sqrt( vx^2 + vy^2 + vz^2 )
> >> >>
> >> >>
> >> >> This is what you are looking for:
> >> >>    ( t' )   ( g         -g*v*nx        -g*v*ny        -g*v*nz     ) ( t )
> >> >>    ( x' )   ( -g*v*nx   (g-1)*nx^2+1   (g-1)*ny*nx   (g-1)*nz*nx  ) ( x )
> >> >>    ( y' ) = ( -g*v*ny   (g-1)*nx*ny    (g-1)*ny^2+1  (g-1)*nz*ny  ) ( y )
> >> >>    ( z' )   ( -g*v*nz   (g-1)*nx*nz    (g-1)*ny*nz   (g-1)*nz^2+1 ) ( z )
> >> >> where
> >> >>    (nx,ny,nz) = unit vector in direction of velocity
> >> >>     v = amplitude of velocity
> >> >>     g = 1/sqrt(1-v^2)
> >> >>
> >> >> In component notation, writing the velocity vector with components
> >> >>     ( vx, vy, vz ) = ( v nx, v ny, v nz )
> >> >> and
> >> >>      v = sqrt( vx^2 + vy^2 + vz^2 )
> >> >> this becomes:
> >> >>   t' = g t - g vx x
> >> >>            - g vy y
> >> >>            - g vz z
> >> >>   x' = -g vx t + (g-1)/v^2 vx vx x + x
> >> >>                + (g-1)/v^2 vx vy y
> >> >>                + (g-1)/v^2 vx vz z
> >> >>   y' = -g vy t + (g-1)/v^2 vy vx x
> >> >>                + (g-1)/v^2 vy vy y + y
> >> >>                + (g-1)/v^2 vy vz z
> >> >>   z' = -g vz t + (g-1)/v^2 vz vx x
> >> >>                + (g-1)/v^2 vz vy y
> >> >>                + (g-1)/v^2 vz vz z + z
> >> >>
> >> >> If you don't like this, then you better find another game to play.
> >> >>
> >> >> Dirk Vdm
> >> >
> >> > I am not disputing the above, I am asking a simple question.
> >> > If vx, vy and vz are not given, then how do I calculate them if v, t,
> >> > x, y and z are given?
> >> > 
> >> > The question is simple enough, so stop hand waving.
> >>
> >> No, you are not disputing the above. You don't understand the
> >> first thing about the above. I think you haven't even read it.
> >> You better find another game.
> >> I repeat:
> >> Doing physics without being fluent in elementary geometry
> >> and algebra is a bad idea.
> >
> > If you're so fluent in elementary geometry and algebra, then why can't
> > you answer the simple question?
>
> The question is answered above.
> You just have to read it.
>
> Dirk Vdm

You have not answered the question at all, and anyone reading this
thread can see that.
Pehaps you should make a guest appearance on your own website.