Re: My Quests on Learning Lorentz Transformation


"Eka Siswanto" <ek4_sisw4nto@xxxxxxxxx> wrote in message news:1141714220.736406.109730@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
If so, how do we arrive at, for example :

delta(x) = A delta(t') + B delta(x') ?

I hope you don't mind my using the D-notation.
Confining us to one dimensional motion, an arbitrary
transformation would look like
{ Dt = Ft( Dt', Dx' )
{ Dx = Fx( Dt', Dx' )
where Ft and Fx are two arbitrary functions of two variables.

But we assume that the transformation is linear, so it looks like
{ Dt = A Dt' + B Dx'
{ Dx = C Dt' + D Dx'
where A, B, C and D are numbers, not depending on Dt' or Dx'.
Those are the special functions Ft and Fx.
They will of course turn out to depend on the relative velocity
between the systems.



Thanks anyway for your hint. It give more breakthrough to be worked at.
I am still working on it to arrive at the above conclusion. I suspect
this has something to do with coordinate transformation using matrix
algebra that I've learnt in high school, but I forgot it.

Yes, the functions Ft and Fx form a linear vector function that
maps a pair of numbers to another pair of numbers:
[t,x] = F([t',x']) = [ F1([t',x']), F2([t',x']) ]
such that
F( [t'1,x'1]+[t'2,x'2] ) = F( [t'1, x'1] ) + F( [t'2,x'2] )
and
F( k [t'1,x'1] ) = k F( [t'1,x'1] )

You can verify that with the above definition. High school indeed :-)

Dirk Vdm


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