Re: why lorentz transformation?


David McAnally wrote:
> "Sue..." <suzysewnshow@xxxxxxxxxxxx> writes:
>
> >David McAnally wrote:
> >> "Sue..." <suzysewnshow@xxxxxxxxxxxx> writes:
> >>
> >> >francisco wrote:
> >> >> galileo's principle of relativity states that the laws of mechanics should
> >> >> be the same for all inertial observers. and indeed, newtonian mechanics is
> >> >> unchanged under galilean transformations. the problem is that maxwellian
> >> >> electrodynamics is not the same in every inertial frame under that
> >> >> transformation. so what to do? find a set of transformations under which
> >> >> both mechanics and electrodynamics are the same for all inertial frames.
> >> >> this leads to the lorentz transformation.
> >>
> >> >Since Maxwell's equations don't predict radiation either
> >>
> >> As the softrat points out, Maxwell's Equations do predict the existence of
> >> electromagnetic radiation. What line of reasoning could possibly have led
> >> you to believe that they don't? Seeing that you have made this
> >> demonstrably false claim about Maxwell's Equations, how could anybody
> >> trust your word on anything else?
>
> >Science is not the business of knowing who to trust.
> >The line of reasoning is in the two well considered
> >papers offered
>
> At no point in either of those papers was there any statement to the
> effect that Maxwell's Equations do not predict the existence of radiation.
> The first of the papers that you listed was connected to gauges for the
> electromagnetic potential, and the fact that the physical properties of
> the electromagnetic field are not affected by the choice of gauge.
>
> >and you have offered nothing
> >*demonstrable*.
>
> I shouldn't need to demonstrate the fact that Maxwell's Equations predict
> the existence of radiation. The fact is very well documented, and has
> been known since the nineteenth century. If, in the twenty-first century,
> this fact, which has been known for well over 100 years, escapes you, then
> that says more about your incompetence than it says about Maxwell's
> Equations.
>
> I will give a small part of the derivation, although, with your level of
> competence, I have no doubt that it will be a waste of time to explain it
> to you.
>
> In vacuo, and in the absence of sources, Maxwell's Equations reduce to
>
> @E_x/@x + @E_y/@y + @E_z/@z = 0,
>
> @B_z/@y - @B_y/@z = (1/c^2) @E_x/@t,
>
> @B_x/@z - @B_z/@x = (1/c^2) @E_y/@t,
>
> @B_y/@x - @B_x/@y = (1/c^2) @E_z/@t,
>
> @B_x/@x + @B_y/@y + @B_z/@z = 0,
>
> @E_z/@y - @E_y/@z = - @B_x/@t,
>
> @E_x/@z - @E_z/@x = - @B_y/@t,
>
> @E_y/@x - @E_x/@y = - @B_z/@t,
>
> where E_x is the x-component of the electric field, B_x is the x-component
> of the magnetic field, etc, c is a constant with the dimensions of speed
> (with known value 299 792 458 m s^{-1}), and for any field f, @f/@x
> denotes the derivative of f with respect to x, etc.
>
> Upon differentiation of the first equation above with respect to x, the
> second with respect to r, the seventh with respect to z, and the eighth
> with respect to y, we get
>
> @^2 E_x/@x^2 + @^2 E_y/(@x @y) + @^2 E_z/(@x @z) = 0,
>
> @^2 B_z/(@t @y) - @^2 B_y/(@t @z) = (1/c^2) @^2 E_x/@t^2,
>
> @^2 E_x/@z^2 - @^2 E_z/(@z @x) = - @^2 B_y/(@z @t),
>
> @^2 E_y/(@y @x) - @^2 E_x/@y^2 = - @^2 B_z/(@y @t).
>
> By an appropriate linear combination of these four statements, it follows
> that
>
> @^2 E_x/@x^2 + @^2 E_x/@y^2 + @^2 E_x/@z^2 = (1/c^2) @^2 E_x/@t^2.
>
> This is just the statement that E_x satisfies the wave equation.
> Similarly, E_y,E_z, B_x, B_y and B_z satisfy the wave equation. This
> immediately implies the existence of electromagnetic radiation which
> moves at a speed of c.
>
> Alternatively, in vacuo and in the absence of sources,
>
> div E = 0,
>
> curl B = (1/c^2) @E/@t,
>
> div B = 0,
>
> curl E = - @B/@t.
>
> It follows that
>
> curl curl B = (1/c^2) @(curl E)/@t = - (1/c^2) @^2 B/@t^2,
>
> and
>
> curl curl B = grad div B - del^2 B = - del^2 B,
>
> where del^2 is the Laplacian operator, i.e.
>
> del^2 f = @^2 f/@x^2 + @^2 f/@y^2 + @^2 f/@z^2.
>
> It follows that del^2 B = (1/c^2) @^2 B/@t^2. Similarly,
> del^2 E = (1/c^2) @^2 E/@t^2. So both E and B satisfy the
> wave equation, and so the existence of electromagnetic
> radiation automatically follows from these considerations.
>
> -----

I don't see any 1/r^2 term in your work.
Try again:
http://arxiv.org/abs/physics/0204034

Sue...

.

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