Dirk Van de moortel <dirkvandemoortel@nospAm.hotmail.com> wrote in message
  _%tEk.27069$%54.21562@newsfe28.ams2
> Stamenin <tasko.s@hotmail.com> wrote in message
>  2ea6185f-cab9-4f61-af3c-15abffbfff2d@34g2000hsh.googlegroups.com
>> On Sep 29, 11:40 pm, "Dirk Van de moortel"
>> <dirkvandemoor...@nospAm.hotmail.com> wrote:
>>> Stamenin <task...@hotmail.com> wrote in message
>>>   d1881525-36ad-4e3c-b854-1961f02a6...@w7g2000hsa.googlegroups.com
>>> 
>>> [snip]
>>> 
>>>> This example is again an algebra and not a derivation.
>>> 
>>> If you would have looked a bit further, you would have seen
>>> when the derivation happened, but never mind, that was not
>>> my point.
>>> 
>>>> You have dx1/dt1 in one side and dx2/dt2 in the other side and this is
>>>> not the same with the dx1/dt in the left side in case of the GT and
>>>> dx2/dt in the right side. Any way I asked you about the comparative
>>>> results obtained by the two transformations and have no an answer.
>>> 
>>> I gave you the answer. I will repeat it below.
>>> You can point out where you think the error is.
>>> 
>>> These are your equations:
>>>    |--------
>>>    |   2) The Lorentz transformation is:
>>>    |        x1=(vt2+x2)/R              (2)
>>>    |        x2=(x1-v.t1)/R             (3)
>>>    |        t1=(t2+v.x2/c^2)/R         (4)
>>>    |        t2=(t1-v.x1/c^2)/R         (5)
>>>    |       Where R=(1-v^2/c^2)^0.5.
>>>    |   ...
>>>    |   2-1) For the Lorentz transformation we can use only the first method
>>>    |   by dividing de relation (2) with the relation (4) and (3) with (5).
>>>    |   The derivation method doesn’t work in this case and this is a minus
>>>    |   for the LT because it shows that the LT is in contradiction with
>>>    |   differential mathematics.
>>>    |   x1/t1=(v.t+x2)/(t2+v.x2/c^2) or,
>>>    |        v1=(v+v2)/(1+v.v2/c^2)     (8).
>>>    |        v2=(v1-v)/(1-v.v1/c^2)     (9).
>>>    | ...
>>>    |   Sorry but in your calculus you didn’t take in to account the
>>>    |   following:
>>>    |        t1=(t2+v.x2/c^2)/R  and  dt1/dt2=(1+v.v2/c^2)/R
>>>    |        t2=(t1-v.x1/c^2)/R  and  dt2/dt1=(1-v.v1/c^2)/R
>>>    |   Because of that dt1/dt2 is not equal with dt2/dt1 and you are
>>>    |   wrong putting
>>>    |   dt2/dt1=R/(1+v.v2/c^2). This is a consequence of the fact that
>>>    |   t1 is not equal with t2.
>>>    |--------
>>> 
>>> We take YOUR
>>>      t1=(t2+v.x2/c^2)/R   and   dt1/dt2=(1+v.v2/c^2)/R         (A)
>>>      t2=(t1-v.x1/c^2)/R   and   dt2/dt1=(1-v.v1/c^2)/R         (B)
>>> and start from YOUR equation (B):
>>>      dt2/dt1 = ( 1 - v v1/c^2 ) / R           [C]
>>> and see what we get when we calculate the inverse of this.
>>> 
>>> Form (C) we get:
>>>      1 / (dt2/dt1) = R / ( 1 - v v1/c^2 )             [D]
>>> 
>>> Then, from YOUR equation (8), we insert the value of v1
>>>      v1 = ( v + v2 ) / ( 1 + v v2/c^2 )
>>> into [D] to get
>>>      1 / (dt2/dt1)
>>>          = R / [ ( 1 - v/c^2 ( v + v2 ) / ( 1 + v v2/c^2 ) ) ]
>>>          = R / [ ( 1 + v v2/c^2 - v/c^2 ( v + v2 ) ) / ( 1 + v v2/c^2 ) ]
>>>          = R / [ ( 1 + v v2/c^2 - v^2/c^2 - v v2/c^2 ) / ( 1 + v v2/c^2 ) ]
>>>          = R / [ R^2 / ( 1 + v v2/c^2 ) ) ]
>>>          = ( 1 + v v2/c^2 ) / R .
>>> Ok, so we started from your equations and we found
>>>      1 / (dt2/dt1) = ( 1 + v v2/c^2 ) / R .
>>> 
>>> And your equation (A) says that
>>>      dt1/dt2=(1+v.v2/c^2)/R
>>> 
>>> So, indeed, like I said:
>>>      dt2/dt1 = R / ( 1 + v v2/c^2 )
>>> and
>>>      1 / (dt2/dt1) = dt1/dt2
>>> and
>>>      (1+v.v2/c^2)/R = R / (1-v.v1/c^2)
>>> 
>>> What exactly do you think is wrong with this and why?
>>> 
>>> Dirk Vdm
>> 
>> I think you have to take the two relations fo one direction of the LT.
>> 
>>   x1=(x2+vt2)/R       (1) and,
>>   t1=(t2+v.x2/c^2)/R  (2)
> 
> I *have* taken them when they were called (2) and (4):
>    |     x1=(x2+vt2)/R       (2) and,
>    |     t1=(t2+v.x2/c^2)/R  (4)
> 
> Repeat from my first reply to your original post:
> 
> From YOUR
>          x1 = (v t2 + x2 ) / R            (2)
> taking the derivate w.r.t. t1:
>          dx1/dt1 = (v dt2/t1 + dx2/dt1 ) / R ,
> using the chain rule dy/dx = dy/dz dz/dx :
>          dx1/dt1 = (v dt2/t1 + dx2/dt2 dt2/dt1 ) / R ,
> and using the definitions of v1 and v2 ,
>          v1 = (v dt2/t1 + v2 dt2/dt1 ) / R
> and isolating the common factor
>          v1 = dt2/dt1 (v + v2 ) / R           (8')

     Here v1 = dx1/dt1 = d/dt1(x2+vt2)/R = (d/dt1).(dt1/dt2)(x2+vt2)/R
                       = d/dt2(x2+v.t2)/R = (v2+v)/R
  This is done in accord with the caine roul as you say. Do not
complicate more this problem and I do not like to enter in permanent
contradictions with you. Fact is that the LT is a big problem and it
has done a big mess in physics. Mine intention with this topic is to
show that the LT is an approximation of the GT and I am satisfied that
it is realized that not questinable. Do not ask me to correct any
mistake in your calculus.

> 
> O.t.o.h from YOUR
>           t1 = ( t2 + v x2/c^2 ) / R         (4)
> taking the derivate w.r.t. t2:
>          dt1/dt2 = ( dt2/dt2 + v dx2/dt2 .c^2 ) / R ,
> using the def. of v2 and fact that dx/dx = 1 ,
>          dt1/dt2 = ( 1 + v v2 /c^2) / R
> and using the inverse derivative property dy/dx = 1 / (dx/dy):
>          dt2/dt1 = R / ( 1 + v v2 /c^2 ) ,
> and inserting this into (8'):
>          v1 = ( v + v2 ) / ( 1 + v v2/c^2 )
> which is your equation (8)
> 
> Do you ever look at what I write?
> 
> Dirk Vdm